The niceness conjecture for Boolean lattices

Let $B_n$ denote the Boolean lattice of subsets of an $n$-element set, and let a poset be nice when its incomparability graph has the nice property. Boolean-lattice niceness conjecture. The Boolean lattices $B_n$ are nice. This is a reformulation of a problem proposed by Graham, as observed by Stanley. The supplied text gives no resolution, so the conjecture remains open.