Just what the title says. And how big is it?
e: “uninhabited” is probably a better word for the question, actually.
You might run into a problem with the term “forest”. Most of Alaska is government owned and Canada has some mega-big territory that is uninhabited all the way into the Arctic Circle. Much of this turns into tundra and then plain ice as you go north however. Siberia is the same. In the lower 48, Maine has massive amounts of true uninhabited forest. The Amazon basin may be a good place to look as well.
The title seems to be claimed by the:
*Tambopata Candamo Reserved zone was established in 1990 with an area of 1,043,998 hectares. It is located in Departments of Madre de Dios and Puno. (Southeastern Peru) at an altitude between 500m to 2800m (1640 feet to 9186 feet)
Tambopata Candamo is the world’s largest uninhabited jungle and it is considered one of the areas least disturbed by man. *
Nouabalé-Ndoki National Park in the Congo claims about 400,000 uninhabited hectares. The forest in Minkébé National Park in Gabon says they have about 300,000 hectares ( the larger park is more than twice that size ). As those are among the most remote and largest tropical forests in the world outside of South America, I suspect the TC wins.