Gottfried Heinrich Bach (26 February 1724 – 12 February 1763) was the firstborn son of Johann Sebastian Bach by his second wife Anna Magdalena Wilcke. Born in Leipzig, Gottfried Heinrich became "feeble-minded" (mildly mentally handicapped in some way) at an early age, but he played the keyboard well and C. P. E. Bach is quoted as saying that he showed "a great genius, which however failed to develop". According to some sources he composed music.
After his father's death in 1750 Gottfried Heinrich lived with his younger sister Elisabeth Juliane Friederica and her husband Johann Christoph Altnickol. Altnickol was a musician who lived and worked in Naumburg approximately 60 km (37 mi) southwest of Leipzig. After his brother-in-law's death in 1759 Gottfried Heinrich stayed on in Naumburg with his sister until his own death a few years later.