^1939, if I remember correctly, although they are now claiming at least two more, based on some kind of retroactive awarding of championships. Kind of like how Bama claims 12 (more?) national titles.
From Wikipedia:
[h=4]National championships (3)[/h]Until 2012 Texas A&M claimed just one national title, voted No. 1 by the AP Poll shortly after its inception along with No. 1 in 8 of the 12 other major polls, after the 1939 season.Southern California also claim this title through the Dickinson System;[SUP][6][/SUP] however, this was the only poll that year in which USC finished No. 1.[SUP][7][/SUP][SUP][8][/SUP] In 2012, Texas A&M added claims to two additional national championships.[SUP][9][/SUP][SUP][10][/SUP] The 1919 team finished 10–0–0 and unscored upon, earning a retroactive national title by ten selectors, including the Billingsley Report and National Championship Foundation.[SUP][11][/SUP][SUP][12][/SUP] The 1927 team finished 8–0–1, with a tie against TCU in Fort Worth, Texas, earning a retroactive national title by the Sagarin Rating and the Sagarin ELO-Chess.[SUP][13][/SUP] Additionally, the 1917 team finished 8–0–0 and unscored upon, earning a retroactive national title by 1st-N-Goal and James Howell, but Texas A&M does not claim this as a national championship.[SUP][14][/SUP]
The prevailing rumor in Aggieland was that this billboard was put up by Texas fans to piss us off. They don't go by Aggie Nation and the billboards owner got a cease and decist from TAMU about this board. FYI.