In a large bowl, mix together the yogurt, lemon juice, tandoori masala, ginger paste, garlic paste, salt, cayenne pepper, paprika, garam masala, and vegetable oil.
Add the chicken pieces to the marinade and coat them well. Cover the bowl and let it marinate in the refrigerator for at least 2 hours, or preferably overnight.
Cooking:
Preheat your grill to medium-high heat.
Thread the marinated chicken pieces onto skewers and place them on the grill. Cook for about 15-20 minutes, turning occasionally, until the chicken is cooked through and has a nice charred appearance.
Garnish with fresh cilantro and serve hot with naan bread and raita on the side.