(c. 1644 -19 May 1676) was an English portrait painter, a pupil of Peter Lely, who approached his teacher in artistic excellence, but whose life was cut short by a dissolute lifestyle.
Greenhill was born at Salisbury, Somerset (now Wiltshire) around 1644, the eldest son of John Greenhill, registrar of the diocese of Salisbury, and Penelope Champneys, daughter of Richard Champneys of Orchardleigh, Somerset. His grandfather was Henry Greenhill of Steeple Ashton in Wiltshire. His father was connected through his brothers with the East India trade.
Greenhill's first attempt was a portrait of his paternal uncle, James Abbott of Salisbury, whom he is said to have sketched surreptitiously, as the old man would not sit for him. About 1662 he moved to London, and became a pupil of Sir Peter Lely. His progress was rapid, and he acquired some of Lely's skill and method. He carefully studied Vandyck's portraits, and George Vertue commented that he copied so closely Vandyck's portrait of "Thomas Killigrew and his dog" that it was difficult to know which was the original. Vertue also says that his progress excited Lely's jealousy.
Greenhill was at first industrious, and married early. But a taste for poetry and drama, and living in Covent Garden in the vicinity of the theatres, led him to associate with many members of the free-living theatrical world, and he fell into "irregular habits". On 19 May 1676, while returning from the "Vine Tavern" (in Holborn) in a state of intoxication, he fell into the gutter in Long Acre, and was carried to his lodgings in Lincoln's Inn Fields, where he died the same night. He was buried in St Giles in the Fields church. He left a widow and family, to whom Lely gave an annuity.