In medium bowl, whisk together coconut milk and curry paste till smooth. Stir in cilantro, chicken, carrots, green onions and peanuts. Toss to coat.
Arrange tortillas in single layer on flat surface. Place one quarter of chicken down center of each tortilla. Top with lettuce. Roll up tortillas burrito-style, tucking ends in and wrappeing each up snugly. Cut each in half. Serve immediately or wrap in plastic wrap and refrigerate.