The race takes its name from the racehorse, Thyestes, by The Tetrarch (out of Tetratema), was bred by Major Victor McCalmont of Mount Juliet and trained by Atty Persse at Stockbridge, Wiltshire. Thyestes was rated the third-best two-year-old of 1930 as a result of his winning his only two races, the National Breeders Produce Stakes over 5 furlongs at Sandown Park and the Rous Memorial Stakes over 6 furlongs at Goodwood. Thyestes never ran again due to injury and was retired to stud in Yorkshire. The Thyestes trophy was presented to the Kilkenny Show by Major Dermot McCalmont for a 5-year-old likely to make a good hunter. The trophy was won by a horse owned by Mr John McEnery of Rossenarra Stud, Kells, County Kilkenny and ridden by his son Martin. The McEnery family then presented it to Gowran Park for the first running of the Thyestes Chase in 1954
The race is usually contested by horses who go on to run in the Grand National and has been won in recent years by two horses who have gone on to win the Grand National, in Hedgehunter and Numbersixvalverde. In recent years horses who have won the Goffs Thyestes Chase have gone very close in the Cheltenham Gold Cup with Djakadam & On His Own both finishing being just pipped at the post.