Put the mango, cilantro, lemon juice, vinegar, oil, garlic, chipotle, salt and pepper in a food processor and puree until smooth. Adjust seasonings to taste.
Add the chicken with half of the chipotle-mango sauce to a resealable plastic bag, and massage to coat the chicken with the sauce. Refrigerate at least 6 hours to marinate.
Put the other half of the chipotle-mango sauce into a small saucepan and simmer over low heat until thick, stirring often, about 15 minutes. Set some of the simmered sauce aside to serve on the side, and baste the chicken every few minutes with the rest of the sauce.
Preheat a grill or grill pan to medium-high heat and brush with oil. Remove the chicken from the marinade and put on the grill.
Grill the chicken, turning and basting about every 5 minutes, until cooked through, 20 to 25 minutes. Transfer to a serving platter and serve with the reserved chipotle-mango sauce.