No, he is constitutionally allowed to run for the office. He is profoundly unqualified for the job.
Outside of Constitutional parameters, to say that Obama is "profoundly unqualified" is a profound understatement. Sure, most civilized humans understand that Obama is nothing more than an over-hyped, flavor-of-the-month scumbag, but worse than merely being "profoundly unqualified", Obama is a serious threat to the very existence of our nation as we know it.
We have seen how long it takes to recoup our military strength and regain credibility internationally after recent rat administrations, but the future under an Obama Administration could be even more damaging. And the damage that that p.o.s. Obama could do with a few Supreme Court nominations sends shivers down my leg.