Lichtman's conjecture on free subgroups in division rings

Let $D$ be a division ring, and write $D^\times$ for its multiplicative group. A group is noncyclic free if it is a free group that is not cyclic. Lichtman's conjecture. The group $D^\times$ contains a noncyclic free group. This conjecture concerns the existence of free multiplicative structures in division rings; the source gives no resolution status.