A yogurt marinade produces extremely tender meat. The longer these drumsticks marinate, the deeper their flavor. Slideshow: More Curry Recipes
In a large bowl, stir together the yogurt, lime juice, curry powder, salt and pepper. Add the chicken and toss until thoroughly coated in the yogurt mixture. Transfer to a resealable plastic bag and seal tightly, pressing out any air, then refrigerate for at least 1 hour and up to 24 hours.
Heat a grill over moderate heat. Lightly oil the grill rack and grill the chicken legs until the underside is well browned, about 10 minutes. Flip the chicken and continue to cook, turning occasionally, until browned all over and just cooked through, about 15 minutes more.
Serve the chicken legs with lime wedges and cilantro.