A current challenge in the processing of 2D materials, or "van der Waals (vdW) solids", is the transfer of 2D layers from source crystals and growth substrates onto target substrates. Transfer - as opposed to direct growth and patterning on the target - enables low-temperature processing of the target as well as the use of diverse target materials. These two attributes will allow the assembly of vdW heterostructures to realize devices exploiting the unique properties of vdW materials. Until now, however, there has been no effective method for transferring regions of monolayer material of controlled shape from a multilayer source. We introduce such a method and demonstrate its use in the spatially controlled transfer of arrays of single-layer MoS2 and WS2 sheets from multilayer crystals onto SiO2 substrates. These sheets have lateral sizes exceeding 100 μm and are electronically continuous. The method offers a scalable route to parallel manufacturing of complex circuits and devices from vdW materials.