Henry Cheyne, 1st Baron Cheyne (31 May 1540 – 3 September 1587) was an English politician. Henry Cheyne was the son of Sir Thomas Cheyne of Shurland in the Isle of Sheppey, Kent, by his second wife, Anne Broughton (d. 16 May 1562), daughter of John Broughton (d. 24 January 1518) of Toddington, Bedfordshire, and Anne Sapcote (d. 14 March 1559), and granddaughter of Sir Robert Broughton by his first wife, Katherine de Vere, said to have been the illegitimate daughter of John de Vere, 13th Earl of Oxford.