April 26, 2005 05:00 PM

Flying in the face of rumors of trouble in their marriage, Jessica Simpson and Nick Lachey have purchased a new $1 million condominium in Las Vegas, PEOPLE has learned.

The couple’s yet-to-be-built luxury 1,200-sq.-ft. digs will be in a new residential complex that will be part of the Palms Resort and Casino off the Vegas strip.

Also featured in the property by casino mogul George Maloof Jr.: a basketball suite, a state of the art recording studio and an exclusive spa.

Simpson and Lachey, who recently wrapped up the third and final season of their MTV reality show Newlyweds, have been dogged by rumors – which they deny – of a growing rift between them. But they and aren’t shying from making future plans together: Their condo isn’t scheduled for completion until 2007.

Meanwhile, the pair have been overseas visiting troops with the USO and performing for an ABC television special set to air in May. Wayne Newton, who chairs the USO’s celeb wing, says the couple’s military connection won’t end with the trip. Says Newton: “I’m sure they’ll bring home messages for (soldiers’) family members.”

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