He would be open to repealing it:

Barack Obama says if elected president he will not require that his Joint Chiefs of Staff be opposed to the “don’t ask, don’t tell” policy that prevents gays from serving openly in the military.
The Democratic presidential front-runner favors repealing the policy, which was instituted during the Clinton administration. He said his priority for the Joint Chiefs will be that they make decisions to strengthen the military and keep the country safe, not their position on the policy.
“I would never make this a litmus test for the Joint Chiefs of Staff,” Obama said in an interview with The Advocate, a gay newsmagazine.
[…]
Asked what he could reasonably accomplish for the gay community as president, Obama said he can “reasonably see” repeal of the “don’t ask, don’t tell” policy as well as signing legislation to ban workplace discrimination against gays. He said he’d like transgendered people to be covered by the law, but thinks it would be tough to get such legislation through Congress.
Obama also said he’s interested in ensuring that same-sex couples in civil unions get federal benefits.