NU traces the origin of its team back to its first intercollegiate games, a two-game series with Lake Forest College in November 1882.  These two games are the first listed in the Wildcats' game-by-game history in NU's media guide.

However, there are reports (some of less substance than others) of even earlier football games played by NU against teams from outside the university.  Some sources site a game in 1881 against Lake View H.S., a match between NU and Evanston H.S. in 1879, and even a possible game played as early as 1876.

The 1876 game is mentioned in Walter Paulison's book The Tale of the Wildcats.  Paulison, NU's sports publicity director, wrote the book in conjunction with the school's centennial celebration in 1951.  In that book, Paulison writes:

"The first evidence of any football activity at Northwestern appeared in an article in The Tripod of Feb. 24, 1876, which said: 'The trial game of football on Tuesday last enthused the boys so much that they formed a Football Association and intend to give "Old Rugby" a hard time in a scrimmage when they come here again.'  Just who the representatives of 'Old Rugby' were is not known. . . ."

The account in Paulison's book is also given on the NU Archive's football history webpage.  It was not clear if  'Old Rugby' was an organized team, nor if the game played at NU was truly "football" at all (by 1876, the American football game, as played by Harvard and McGill, was different from soccer and from standard Rugby).

I decided to see if I could find any more information about this game, when it was played, and against whom.  According to Paulison, The Tripod's account of the game was written on February 24 and mentioned the game having taken place "last Tuesday."  February 24, 1876 fell on a Thursday, which means that this game would have been played on Tuesday, February 22, 1876.

Not only did Northwestern University play a game on that date, the match was covered in the Chicago Tribune!  The following article comes from the Feb. 23, 1876 Chicago Tribune:

"Yesterday the Chicago Football Club visited Evanston to play a game against the Northwestern University students.  The game was something new to the University men, and no preparation had been made for the visitors in the way of laying out the playing field.  Added to this, the ground was frozen so hard that neither goal-posts or line-stakes could be set up.  It was finally agreed to let the University play twenty men against the Chicago team of fifteen, and get along the best way possible under the circumstances.

"At 3:15 the game was called, the Chicago Captain kicking off.  The college men were evidently at sea in regard to the game, for they let Hornsby follow the ball up, and his next kick took it across the line, enabling him to get a touchdown.  The try at goal was successful-first to the Chicago.  Time, 1 minute 30 seconds.  The second goal was a longer tussle, but finally Curtis got the ball, and after a good run touched it down.  Hornsby again scored a goal from the place kick.  By this time the home players were picking up some of the points of the game, and their greater number made it difficult for the Chicago men to get through such a crowded field.

"L.H. Sullivan secured another touchdown, a good long run, but Hornsby failed to get the ball between the goal-posts.  Before another goal was scored half time was called and ends changed.  After this the original twenty players of the University team increased so alarmingly in number that getting through with the ball was an impossibility, and loose scrimmages took place over the entire field, but mainly in the University half.

"C.J. Williams at last scored a goal from a free kick opposite goal.  A second time the same player essayed a free kick, but from a more difficult position, and he failed, owing to the wind carrying the ball off. 

"The game was prolonged a quarter of an hour over the hour agreed upon, and when called the score stood 3 goals for Chicago, to nothing for the University.  The latter, though beaten, have some good material to make a team from if they will practice the game under the rules. . . . "

It seems clear that NU did, indeed, play a verifiable American football game, against an amateur team from Chicago in February 1876.  That the opponent was not another college should not matter: NU officially records its games with other amateur teams during the 1880s and '90s.  If  the 1876 game is recognized by the University, this would push back the official origin of NU football over six years, three years before Michigan's heralded debut on the field, and would give NU the claim as the oldest football team in the Big Ten, if not the midwest.