Depends on how you put it. The oldest alliance in the world is the Anglo-Portuguese alliance, dating back to 1386. England/ Great Britain have been allies with Portugal since then.

But specifying military alliance, (even though Portugal and England did assist each other militarily) One could argue that that Inter-American treaty of Reciprocal Assistance is older, having been signed in 1947, while NATO was signed in 1949. However, there are countries that have left that treaty, such as Nicaragua, Mexico, and Bolivia, and several incidents where countries invoked the treaty but were not supported, such as the Falklands War and the Iraq war, so one could argue that the treaty has not been sufficiently honored and is no longer in effect. You can read more about the individual treaties at these links

http://www.oas.org/juridico/english/sigs/b-29.html

http://www.nato.int/history/nato-history.html

http://www.angloportuguesesociety.org.uk/alliance-history

TL:DR Depends on the definition and whether you would count treaties that have been invoked but not honoured, but possibly yes, probably no.