We describe a method for forming an array of microdroplets between two plates, at least one of which is patterned with a lattice of wetting patches, using a second immiscible fluid to control droplet formation. The method may be useful for performing multiple, small-volume biochemical reactions in parallel, We analyze the forces responsible for droplet formation, describe results of a computer simulation using Surface Evolver, and derive an analytic criterion for droplet formation in terms of the contact angles of the droplet:second fluid interface on the wetting patches and surrounding surface, the diameter of the wetting patches, the distance between wetting patches, and the distance between the plates.