The board of the tiny, rural Texas district of Harrold, near the Oklahoma border, thinks so.
It unanimously approved such a plan, to take effect this fall -- and the move appears to be the first of its kind in the United States.
Though the district only has one school and about 100 students, the policy could have massive reppercussions.
Board members note that the school is about a half-hour's drive from the nearest Sheriff's office.
But foes of the idea worry about the guns getting into the wrong hands.
On The Early Show Tuesday, the superintendent of the district, David Thweatt, who is very much in favor of the plan, went back-and-forth over it with the president of the Houston Federation of Teachers, Gayle Fallon, who vehemently opposes it: