Microsoft has told Eurogamer that it's aware of a few incidents of "unauthorised access" and is working with the relevant individuals to remedy the situation.
However, the spokesperson insisted there is no evidence of a wider Xbox Live security issue. Here is its statement in full:
"We do not have any evidence the Xbox Live service has been compromised. We take the security of our service seriously and work on an ongoing basis to improve it against evolving threats.
"However, a limited number of members have contacted us regarding unauthorised access to their accounts by outside individuals. We are working with our impacted members directly to resolve any unauthorised changes to their accounts.
"As always, we highly recommend our members follow the Xbox LIVE Account Security guidance provided at www.xbox.com/security to protect your account."