Nick Lachey's New Gal

05/31/2006 at 02:20 PM EDT

What's left of Nick Lachey six months after the breakup of his marriage to Jessica Simpson? Plenty, it seems. The singer – while managing to escape the attention of the press – has been dating stylist Kim Kardashian for the past month, sources tell PEOPLE.

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The twosome chatted the night away at Hollywood hot spot Shag May 15 and were photographed May 24 at an afternoon showing of The Da Vinci Code in Westwood. (The pair held hands as they exited the theater, but separated when photographers started snapping.)

"They're sweet on each other," a source close to the couple tells PEOPLE. "It's the beginning stages of a relationship." (His rep had no comment.)

What's the attraction? Friends point out that Lachey, 32, and Kardashian, 25 – who met at a party for Arizona Cardinals quarterback Matt Leinart last month – have at least one thing in common: failed marriages. Kardashian, whose father is the late O.J. Simpson trial attorney Robert Kardashian, divorced music producer Damon Thomas in 2004.

"Part of the attraction is they have both gone through similar life situations," says the source. "They developed a bond."

Still, Lachey may be going slow. "For Nick to settle down," says a pal, "it will take someone who is a lifelong partner."