Rachel Bilson Sells L.A. Home -- Hayden Christensen Moves Out

Hayden Christensen is hauling his stuff out of his fiancee Rachel Bilson's L.A. house -- and he's bringing her crap with him -- because the "OC" actress just sold the place for big money.

Sources close to Bilson tell us, Rachel recently attempted to sell the house, but took it off the market when she didn't get the offer she was looking for.

We're told that changed very recently -- when a prospective buyer re-approached Bilson with a heftier offer on the home ... an offer that was so good, Bilson just couldn't turn it down .. so she and Hayden are moving out.

We're told Bilson is currently looking for a replacement.