Whisk together marinade ingredients in a large bowl. Add chicken and toss to combine evenly with marinade mixture. Cover and refrigerate for at least 30 minutes, or up to 8 hours.
When ready to cook, preheat grill to medium-high. Arrange chicken pieces on hot grill, then discard marinade.
Grill for 6-10 minutes on each side, or until cooked through. Serve with lime wedges and cilantro, if desired.
For the cucumber-mint sauce:
Peel cucumber and finely grate over a paper towel to soak up excess moisture. In a bowl, stir yogurt, cumin, garlic, and cilantro or mint leaves. Cover and refrigerate at least 30 minutes before serving, to allow flavors to marinade.
Spoon over grilled chicken or serve on the side.
Notes
Grilled chicken adapted from Recipe Critic | Cucumber sauce adapted from Epicurious