Microsoft attributed the problem to a huge influx of new gamers during the holiday period, and had offered a free Xbox Live Arcade game to all subscribers by way of apology.
However, Orlando Perez, Shannon Smith and Keith A Kay filed the suit in a US District Court in the Southern District of Texas alleging breach of contract.
The action claims that Xbox Live "crashed and prevented Plaintiffs around the world from accessing online play for several weeks" in December 2007.
"In the last three months of 2007, Microsoft sold over four million Xbox console units. This increase in console purchases led to a substantial increase in Xbox Live subscriptions," the suit continues.
"Microsoft knew [that] the increase in subscriptions would increase game-play on its servers yet failed to provide adequate access and service to Xbox Live and its subscribers."
A Microsoft spokesman said that the firm had only recently learned of the lawsuit and was "not in a position to comment at this time".
The suit claims that an "implied warranty existed between Defendant and Plaintiff regarding the Xbox Live subscription" but that the service "was not fit for the ordinary purposes for which such goods are used".
The document also claims that Microsoft "failed to exercise reasonable care or competence in communicating information regarding the nature of the services offered through Xbox Live".
The suit seeks unspecified damages including expenses associated with Xbox Live memberships as well as an award of attorney fees and costs.
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