Preheat a grill to medium (350° to 450°) with an area left clear or a burner turned off for indirect heat.
In a blender, whirl 1/2 cup water, 1 1/2 cups cilantro, 1 1/2 chiles, the coconut, mint, lemon juice, sugar, salt, garlic, and cumin until fairly smooth.
Cut 4 sheets of parchment paper, each 12 in. square. Fold each in half and cut out a half-heart to edges, with center on fold line. Lay parchment hearts open on a work surface. On each, set a chicken piece in center just to right of fold line, smear all over with 2 tbsp. sauce, and fold under any thin parts so chicken is evenly thick. Fold hearts closed. Starting at top of each heart and continuing around and down to the tip, roll curved edges tightly toward chicken, rolled side up, tucking the point of the heart into the folds to make a snug packet.
Grill packets over indirect heat until an instant-read thermometer inserted through parchment into center of chicken reaches 160° to 165°, 15 to 20 minutes.
Transfer chicken from packets to plates and pour juices on top. Thinly slice remaining 1/2 chile. Scatter chile and small cilantro sprigs over chicken and serve more sauce on the side.