In 1983, Chenery, Martha F. Gerry, and Allaire du Pont became the first women to be admitted as members of The Jockey Club. From 1976 to 1984, Chenery served as president of the Thoroughbred Owners and Breeders Association. Also in 1976, she became a member of the Executive Committee of the American Horse Council, the horse industry trade association in Washington, DC. She also served as a member of the judges' panel of the Jockey Club, which bestows the Dogwood Dominion Award. In addition, she helped found the Thoroughbred Retirement Foundation, an organization dedicated to saving Thoroughbred horses no longer able to compete on the racetrack from possible neglect, abuse and slaughter.