Uma filling date book

It hasn’t taken beautiful Kill Bill star Uma Thurman long to fill up her date book since splitting with hubbie Ethan Hawke.

Friends of handsome hotelier Andre Balazs, owner of LA’s ultra-hip Chateau Marmont, Mercer and Standard hotels, reveal that he and Uma have been seeing a lot of each other lately.

Thurman and Hawke, both 33, separated after five years of marriage and two children, after claims that he was openly dating a Canadian model, Jen Perzow.