Spread a little of the pesto down the center or each wrap. Arrange a small handful greens and tomatoes in the center and season to taste. Layer with chicken, cheese, and any other fillings of you choice. Fold the top and bottom edges inward followed by one side.
Continuing in that direction, roll up the wrap, burrito-style, until closed. Seal with two toothpicks and slice down the middle. Serve with additional pesto for dipping. If desired, slice into thinner pieces, spear each piece with a toothpick and serve as an appetizer.