To make the salsa: Place tomatillos and chile on a grill screen or basket set over direct-heat area of grill (the vegetables will fall through without it). Cook, turning as needed, until well charred on all sides, about 3 minutes. Transfer tomatillos and chile to a blender, add lime juice and 1 tablespoon olive oil, and pulse until combined but still chunky. Transfer to a bowl, fold in cilantro, and season with salt. Makes about 2 cups. (The salsa can be made up to a week in advance and refrigerated. Bring to room temperature before serving.)
To grill the chicken: Place thighs, meaty side down, over indirect-heat area of grill. Cook, turning once, until thighs are nicely grill-marked on both sides and firm to the touch, about 10 to 15 minutes per side. Check internal temperature with a meat thermometer inserted into thickest part of thigh away from the bone; when done it should be 170 degrees. Try to turn thighs only once so they develop nice grill marks.
Transfer thighs to a platter and let rest for 10 minutes. Serve at once with salsa.
Nutrition information per each of 8 servings:
Calories265Fat17 gSodium85 mg
Carbohydrates4 gSaturated fat4 gTotal sugars2 g