  A finite simple graph \G determines a right-angled Artin group G_\G, with one
generator for each vertex v, and with one commutator relation vw=wv for each
pair of vertices joined by an edge. The Bestvina-Brady group N_\G is the kernel
of the projection G_\G \to \Z, which sends each generator v to 1. We establish
precisely which graphs \G give rise to quasi-K\"ahler (respectively, K\"ahler)
groups N_\G. This yields examples of quasi-projective groups which are not
commensurable (up to finite kernels) to the fundamental group of any
aspherical, quasi-projective variety.
