Having received his Diploma in Education from Oxford, Chesshyre did not enter the teaching profession, but instead was appointed in 1967 to a position as an assistant at the College of Arms. He was a Green Staff Officer at the Investiture of the Prince of Wales in 1969. Appointed a member of the Chapter of the College of Arms the following year, he served as Rouge Croix Pursuivant (1970–78), Chester Herald (1978–95), Norroy and Ulster King of Arms and Principal Herald of the North part of England and of Northern Ireland (1995–97), and Clarenceux King of Arms and Principal Herald for the South, East and West parts of England (1997–2010). From 1971 until 1978 he also served on the staff of Anthony Wagner. He was Registrar of the College of Arms from 1992 until 2000 and was the Founder Secretary of the College of Arms Uniform Fund in 1980, serving in that capacity until 1999. From early in his career Chesshyre from time to time served as a deputy to Garter Principal King of Arms for the purpose of introducing peers into the House of Lords. For example, in 1975 he introduced Baroness Vickers.