The "Kill Bill" star became a mother for the third time on July 15 when she delivered a little girl and her first child with financier boyfriend Arpad Busson, reported TMZ online.
Thurman, 42, was spotted cradling her bundle of joy at an organic cafe store in Woodstock.
"Thurman is a regular visitor at the organic cafe, where she ordered cold-pressed juices," a source said.
Thurman, who has two other kids from her marriage to Ethan Hawke, is yet to confirm the new arrival's name.
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