If the only outlet in the closet now is a 220v outlet (presumably for a dryer), then it will probably not be easy to get a 120v outlet in there. Your best bet would be if there is a light in the closet, and if the neutral wire were carried down to the switch box. Then, you might connect to the hot conductor (ahead of the switch) and the neutral and ground pressent at the box, and install an outlet there. Otherwise, you'll probably need to go to the nearest outlet outside the closet.

BTW, what are you intending to use the outlet for?

Seems a little odd that the laundry closet doesn't already have a 120v outlet for a washing machine...

Jarrod