The Fitton Baronetcy, of Gawsworth in the County of Chester, was a title in the Baronetage of England.

The second Baronet, High Sheriff in 1633, was an officer in the service of Charles II and was briefly Governor of Bristol following that city's fall during the English Civil War.

He left his estate by his will of 1641 to his Irish cousin William Fitton of Awne (Awrice), County Limerick, (grandson of Sir Edward Fitton, Treasurer of Ireland) to the exclusion of his seven sisters and their husbands.

The will was disputed and lengthy legal proceedings followed involving Alexander Fitton, Lord Chancellor of Ireland (son of William) and Charles Gerard, 1st Baron Gerard, son of Penelope Fitton, eldest daughter of the first Baronet.

Settlement of the lawsuit in 1663 passed the estate to Gerard, who was later created Earl of Macclesfield.