Benjamin Chappell was born in London, England on 5 March 1740 to Richard and Rachel Chappell. He was raised an Anglican but, after becoming well acquainted with John Wesley, he converted to Methodism. He became a lay preacher and when he emigrated to Prince Edward Island in 1774, he was the first Methodist to do so. Like many immigrants, Chappell became an indentured servant for a four-year term in exchange for his passage and provisions. Chappell settled in New London with his wife Elizabeth whom he had married in February of that year. They had at least four children: Elizabeth (19 November 1775 - 28 November 1775); Richard (1777-1835); Theophilus (1778 -1847) and another daughter. In 1778, Chappell and his family moved to Charlottetown. As there was no Methodist minister on the Island at that time, Chappell often held prayer meetings of the Methodist Society in his home which was located on the northwest corner of the intersection of Prince and Water Streets.

Chappell was trained as a wheelwright and machinist. He was a skilled craftsman who specialized in constructing spinning wheels, coaches, and sleighs. He was active within his community holding such positions as overseer of public pumps and wells, overseer of streets, overseer of the poor, and undertaker. He was elected to the third House of Assembly in 1779. He was churchwarden for the Anglican church as early as 1788 when he wrote a letter to Governor Edmond Fanning requesting payment for his past several years of service in that position.

Chappell was also one of the early Post Masters of Prince Edward Island. He was first appointed in 1802 at the age of 63 when he succeeded John Ross who had been appointed in 1800. Chappell first served between 1802 and 1807. He was reappointed on 12 November 1812 and continued in that position until his death on 6 January 1825. He was 86 years old. Chappell's son Richard and a granddaughter Elizabeth later also served in the position of post master.