Robert Henry Barnes (2 October 1849 – 1916) was a British–New Zealand chess player.
In 1880, he lost a match to Eugene Delmar (0.5 : 7.5) in New York. Then he played in Germany, at Frankfurt 1884 (4th scoring 7.5/11); at Frankfurt 1887 (5th DSB Congress, Hauptturnier A, 1st scoring 8/9, and Siegergruppe, 5-6th scoring 1/5); at Leipzig 1894 (9th DSB Congress, Hauptturnier A, 1st scoring 5/5, and Siegergruppe, 3rd-5th scoring 4/7); and won at Eisenach (10th DSB Congress) scoring 10.5/14.
He participated in New Zealand championships in the 1911 (7th scoring 5/10), 1913 (4th scoring 7.5/11), 1914 (2nd 10/14) and 1915 (2nd 9/10).