Mix the yogurt, garlic, ginger, lemon juice, curry, cayenne, and salt in a large ziplock bag until well combined. Add the chicken and turn to coat. Marinate the chicken at least 1 hour or up to 24 hours.
Remove the chicken from the marinade (discard the marinade) and grill over medium-high heat , about 12 minutes per side, until cooked thoroughly. Serve immediately.