Sir Hugh Arthur Henry Cholmeley, 3rd Baronet DL, JP (18 October 1839 – 14 February 1904) was a British soldier and politician.
He was the eldest son of Sir Montague John Cholmeley, 2nd Baronet and Lady Georgiana Beauclerk, fifth daughter of the 8th Duke of St Albans. In 1868, he succeeded his father as baronet. Cholmeley was educated at Harrow School. He served then in the Grenadier Guards and eventually reached the rank of Captain. From 1868 to 1880, he was Member of Parliament (MP) for Grantham. He became High Sheriff of Lincolnshire in 1885 and was a Justice of Peace and Deputy Lieutenant for the same county.
On 12 August 1874, he married Edith Sophia Rowley, daughter of Sir Charles Rowley, 4th Baronet. They had four daughters and a son, Montague, who succeeded to the baronetcy.
Cholmeley is commemorated at St Andrew and St Mary's Church, Stoke Rochford, by a stained glass window erected by his widow and children. Further windows in the church were erected, one to his son Montague, the other to Lady Cholmeley.