Whisk yogurt, lemon juice, oil, ginger, garlic, garam masala, cumin, coriander, paprika, salt and cayenne in a bowl. Cut two shallow slashes across the flesh of each thigh and coat with marinade.
Cover and refrigerate for 2 hours; the prep time includes this marinating period. Heat an outdoor grill to about 400°F with direct and indirect cooking areas and clean the grate.
Lift chicken from the marinade, letting excess drip off, and discard the used marinade. Place thighs over indirect heat, cover and cook for 25 to 30 minutes, turning once.
Move over direct heat and cook for 3 to 5 minutes per side until browned in patches and the thickest meat reaches 175 to 185°F. Shift pieces back to indirect heat if they darken before the centers are ready.
Rest for 5 minutes and serve one thigh per person.