I have been a big fan of the God of War franchise since its debut on the PS2 back in 2005.  I loved the accessibility of the game, the right amout of challenge, and the constant feeling like you're some sort of bad ass.  Almost everything in the game that you do oozes intensity or out-right awesomeness.  And while many other games have done QTE's, I still think that this series does it the best.  That's why when I bought by PSP 3000 back in October, this was one of the first games I decided to get (via download). 
 
God of War:  Chains of Olympus is an amazing representation of the God of War console games on the handheld.  While some of the majesty and awesomeness may be slightly diminished from the small PSP screen, it really does manage to capture everything that was cool about God of War and translate it to the handheld.  First of all, the controls are spot on.  I think that the GOW series has some of the most responsive controls in the genre and GOW:  Chains of Olympus is equally as responsive.  While the dodging mechanic is a bit clunkier in the PSP than in the console version, once you get used to it--everything flows.  Most of the combos remain from the PS2 games and the combat just feels right.  I have to say, some of the magics were kind of throw away, but that being said, the only magic that I ever really used in the first 2 games were the lightening one.   
 
Perhaps another staple of the GOW franchise is the scale of the game.  In the console versions, there are many time when Kratos is minuscule next to a huge set piece.  The PSP game is no different.  They managed to recreate that sense of scale that was critical in developing the mood of the console games.  There were plenty of times in the PSP game where I couldn't believe what I was playing in the palm of my hands.  The graphics also fully stand out.  While there might not have been as much enemy variety compared to the console versions--the enemy encounters always seems satisfying at the end.  The boss battles also felt well done and well planned.  While none of the battles compare to the Hydra boss in the 1st GOD, the fights always seemed fair and fun. 
 
Another thing that stands out in the GOW series is the music--and in this regard, this game does not disappoint.  The music is almost exactly the same and what you would want from of GOW game.   
 
One thing that I appreciated in this game is that there were no really annoying portions in the game.  In GOW 1, climbing the wall in Hades was a platforming chore, and I thought that the end fight will all those Kratos's was not well designed.  GOW:  Chains of Olympus has none of these odd bits.  Another type of puzzle this series likes to throw at you are the levels where you have to turn a crank while enemies attack you.  And if you let go of the crank, the platform that you are on starts to move backwards thus loosing you're progress.  I hated these levels.  There was a section on GOW 2 where you had to bring down some sort of platform and the harpies kept spawning and spawning.  If I didn't power up my lightning magic--I probably would have never won the game.  Well, thankfully, Chains of Olympus only has one of these levels, an it is not that bad. 
  
So I have to say that Chains of Olympus was a great game and worthy entry into the GOW franchise.

I have been a big fan of the God of War franchise since its debut on the PS2 back in 2005.  I loved the accessibility of the game, the right amout of challenge, and the constant feeling like you're some sort of bad ass.  Almost everything in the game that you do oozes intensity or out-right awesomeness.  And while many other games have done QTE's, I still think that this series does it the best.  That's why when I bought by PSP 3000 back in October, this was one of the first games I decided to get (via download). 
 
God of War:  Chains of Olympus is an amazing representation of the God of War console games on the handheld.  While some of the majesty and awesomeness may be slightly diminished from the small PSP screen, it really does manage to capture everything that was cool about God of War and translate it to the handheld.  First of all, the controls are spot on.  I think that the GOW series has some of the most responsive controls in the genre and GOW:  Chains of Olympus is equally as responsive.  While the dodging mechanic is a bit clunkier in the PSP than in the console version, once you get used to it--everything flows.  Most of the combos remain from the PS2 games and the combat just feels right.  I have to say, some of the magics were kind of throw away, but that being said, the only magic that I ever really used in the first 2 games were the lightening one.   
 
Perhaps another staple of the GOW franchise is the scale of the game.  In the console versions, there are many time when Kratos is minuscule next to a huge set piece.  The PSP game is no different.  They managed to recreate that sense of scale that was critical in developing the mood of the console games.  There were plenty of times in the PSP game where I couldn't believe what I was playing in the palm of my hands.  The graphics also fully stand out.  While there might not have been as much enemy variety compared to the console versions--the enemy encounters always seems satisfying at the end.  The boss battles also felt well done and well planned.  While none of the battles compare to the Hydra boss in the 1st GOD, the fights always seemed fair and fun. 
 
Another thing that stands out in the GOW series is the music--and in this regard, this game does not disappoint.  The music is almost exactly the same and what you would want from of GOW game.   
 
One thing that I appreciated in this game is that there were no really annoying portions in the game.  In GOW 1, climbing the wall in Hades was a platforming chore, and I thought that the end fight will all those Kratos's was not well designed.  GOW:  Chains of Olympus has none of these odd bits.  Another type of puzzle this series likes to throw at you are the levels where you have to turn a crank while enemies attack you.  And if you let go of the crank, the platform that you are on starts to move backwards thus loosing you're progress.  I hated these levels.  There was a section on GOW 2 where you had to bring down some sort of platform and the harpies kept spawning and spawning.  If I didn't power up my lightning magic--I probably would have never won the game.  Well, thankfully, Chains of Olympus only has one of these levels, an it is not that bad. 
  
So I have to say that Chains of Olympus was a great game and worthy entry into the GOW franchise.

I never liked GoW 1 much, having played it back in the day.  I appreciated some of what it was doing (derivative as it was), but for every good thing it did, it had one average element and one super frustrating element.  I mean even in the first level there's stuff that feels like it wasn't play tested.  (Is tight-rope walking across tiny beams while battling a camera really the best way to represent a bad-ass?)
 
Anyway, on a whim I bought Chains of Olympus last month, and loved it so much I quit playing it to buy GoW Collection, and try to finish the first game first. STILL frustrating, and not something I want to ever play again, but I like having the story down.

Started back in to Chains of Olympus last night, and finished it today. Like you said, it removes all the irritating stuff from the first game...it just leaves the bad-ass stuff. Graphically it's FAR superior to GoW 1 too (even in the Collection version).

So now I'm playing my third GoW game, without taking a break for something else! 2 so far (about 5 hours in) is maybe even more awesome than Olympus...so far also lacks the irritating parts, and like Olympus just feels/plays better. In the Collection version it looks fantastic...I suspect Santa Monica made higher quality art assets for 2 that were used in this version (unless a bunch of the art was redone by the developer porting it, and they only did 2 and not 1...)

Can't wait to get back to 2. Can't wait to play Ghost of Sparta...and of course God of War 3 after that :)

Ghost of Sparta is even better. 

I've got Ghost of Sparta lined up too (in my backlog)...going to take a break after I finish 2 though to space these out a bit LOL.
 
LiquidPrince, I'm referring to parts in the first game where you're basically tight rope walking (stupid on it's own IMO) and then don't even have the camera steady.  They basically removed the "tight rope walking" from Chains of Olympus and GoW2, thankfully (along with 100 other annoying bits that got smoothed out or removed).  For all the hype with David Jaffe, his GoW is by far the worst IMO, although of course it is the first one...but not the first game of that type, and a lot of that stuff SHOULD have been caught by someone during play testing.