The origins of tandoori chicken begins in a restaurant named Moto Mahal in Peshawar, created by it's chef Kundan Lal Gujral, prior to the partition of British India. He experimented by cooking chickens in the Tandoor (clay oven), usually reserved for cooking the local breads such as naan and roti.
These ovens get to a temperature of up to 900 degrees Celsius and are bell shaped, set into the earth and fuelled with wood or charcoal. The result was that Gujral achieved a wonderful succulent chicken with a slightly charred crispy outside.
In 1947, Punjab was partitioned, joining the eastern district joining India and the western district, Pakistan. Peshawar then became part of Pakistan and Gujral then found himself to be amongst the many Hindu refugees fleeing the new Muslim Pakistan. He then started a new restaurant in Delhi and one of his patrons was famously the first Prime Minister of India, Jawaharlal Nehru, who loved it so much that he made it a staple at official banquets.
Spin offs of tandoori chicken led to the popularised British favourite of tikka and tikka masala.