Preheat an outdoor grill to medium. Soak four 12-inch wooden skewers in water for at least 30 minutes.
Whisk the lime juice, 2 cloves garlic and chipotle together in a medium bowl. Season with salt and pepper. Add the chicken, toss well to coat, and set aside for 20 minutes to marinate.
Meanwhile, put the tomatillos in a medium saucepan and cover with water. Bring to a boil and cook until tender, about 7 minutes and then drain. Puree the jalapeno, onion, the remaining 1 clove garlic and 1 teaspoon salt in a blender until smooth. Add the cooked tomatillos and cilantro sprigs and puree until smooth.
Remove the chicken from the marinade and thread onto the soaked skewers. Lightly oil the grill grates. Grill the chicken, flipping often, until cooked through, 4 to 6 minutes. Serve with the salsa verde and warm tortillas.
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