[Mick]

Carlisle Indian school. Coached by Pop Warner.

Phogge is correct!  And good guess, BC, but technically Chicago still has a football team, albeit Division III. 

Carlisle Indian School existed from 1893 to 1917, and (technically) was the first D1 school to drop football.  They also have the highest winning percentage of any school that has dropped football (.646).  They were typically undersized compared to their opponents, so Glenn "Pop" Warner, who coached Carlisle from 1899 to 1903 and 1907 to 1914, was responsible for instituting a number of innovations, including:

1) The first handoff.
2) The first misdirection plays.
3) The first overhand forward pass thrown as a spiral.  In fact, most forward passes in those days only traveled a few yards.  In 1907, Carlisle played the national champion Penn and won 26-6 (Penn won all other games that year).  Carlisle's fullback Pete Hauser not only could throw a tight spiral, he completed one that traveled 40 yards in the air, utterly shocking those in attendance. They beat U of Chicago's Maroons, and Hauser threw a 50 yard TD in that game.

Their listed rival was Harvard, although Harvard beat Carlisle the first 11 times they played. 

One interesting opponent was the U. S. Military Academy (Army). Warner was the coach.  Here's what he told his team before the game, played just 22 years after the last army battle with the Lakota Sioux at Wounded Knee:

"Your fathers and your grandfathers are the ones who fought their fathers. These men playing against you today are soldiers. They are the Long Knives. You are Indians. Tonight, we will know if you are warriors."  Final score was Carlisle 27, Army 6.

To answer the second question, the next university to drop D1 football was the College of Charleston in 1923.  They are still D1 today, competing in 22 men's and women's sports.

[Mick]

Carlisle Indian school. Coached by Pop Warner.

Phogge is correct!  And good guess, BC, but technically Chicago still has a football team, albeit Division III. 

Carlisle Indian School existed from 1893 to 1917, and (technically) was the first D1 school to drop football.  They also have the highest winning percentage of any school that has dropped football (.646).  They were typically undersized compared to their opponents, so Glenn "Pop" Warner, who coached Carlisle from 1899 to 1903 and 1907 to 1914, was responsible for instituting a number of innovations, including:

1) The first handoff.
2) The first misdirection plays.
3) The first overhand forward pass thrown as a spiral.  In fact, most forward passes in those days only traveled a few yards.  In 1907, Carlisle played the national champion Penn and won 26-6 (Penn won all other games that year).  Carlisle's fullback Pete Hauser not only could throw a tight spiral, he completed one that traveled 40 yards in the air, utterly shocking those in attendance. They beat U of Chicago's Maroons, and Hauser threw a 50 yard TD in that game.

Their listed rival was Harvard, although Harvard beat Carlisle the first 11 times they played. 

One interesting opponent was the U. S. Military Academy (Army). Warner was the coach.  Here's what he told his team before the game, played just 22 years after the last army battle with the Lakota Sioux at Wounded Knee:

"Your fathers and your grandfathers are the ones who fought their fathers. These men playing against you today are soldiers. They are the Long Knives. You are Indians. Tonight, we will know if you are warriors."  Final score was Carlisle 27, Army 6.

To answer the second question, the next university to drop D1 football was the College of Charleston in 1923.  They are still D1 today, competing in 22 men's and women's sports.