He was born in Ardeley (then known as Yardley), Hertfordshire. The manor of Ardeley had belonged to St Paul's Cathedral since before the Norman Conquest. Chauncy stated that the manor-house (Ardeley Bury) and demesne had been held for above 200 years by his ancestors, who had had several leases for lives from the Dean and Chapter of St Paul's.
He attended Stevenage Grammar School, then spent a year at Bishop's Stortford Grammar School before going to Gonville and Caius College, Cambridge followed by the Middle Temple.
Although his main residence was at Ardeley Bury, he also lived at Lombard House, Hertford. He held various offices in Hertford, serving as steward of the borough court and recorder.
In 1712, the year he turned 80, Chauncy was involved in one of England's last witch-hunts. The alleged witch, Jane Wenham, lived at Walkern, near Ardeley. Initially, Wenham approached Chauncy as the local justice for help with a claim against a farmer who had called her a witch. Chauncy asked the rector of Walkern to arbitrate, but when complaints about Wenham continued he issued a warrant for her arrest and gave instructions that she be searched for "witch marks". Although no such marks were found, it was decided that there was sufficient evidence for Wenham to be tried at the assize court in Hertford.
Chauncy died in 1719 and is buried in the chancel of St Lawrence Ardeley with other generations of his family. There is a plaque on the wall of the church to commemorate his life.
In about 1680 he began work on his county history, The Historical Antiquities of Hertfordshire. It took him 14 years to write. By 1695 he was seeking 500 subscribers to pay for the costs of printing, and the volume was finally published in 1700. In writing the work Chauncy paid a team of researchers to gather historical anecdotes and determine genealogical lines for him. It was dedicated to its principal sponsor, the third Earl of Bridgewater; and was illustrated by forty-six engravings (thirty-three of them by Jan Drapentier), most of which were bird's-eye views of the seats of the major subscribers.
He had three wives: Jane Flyer (m. 1657), by whom he had three sons and four daughters before her death in 1672; Elizabeth Gouldsmith (m. 1674), a widow, who died in 1677; and Elizabeth Thruston (m. 1679), by whom he had a son and daughter, and who died in 1706.
In 1692, his eldest surviving son, Henry, married Jane Boteler, a marriage of which Sir Henry strongly disapproved: this brought him into a protracted legal dispute with Jane's father, Sir Nicholas Boteler, and a permanent estrangement from his son, who died in 1703. In the family pedigree published in the Antiquities he did not record the marriage.