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We introduce a novel chip fabrication technique called "brick and mortar", in which chips are made from small, pre-fabricated ASIC bricks and bonded in a designer-specified arrangement to an inter-brick communication backbone chip. The goal of brick and mortar assembly is to provide a low-overhead method to produce custom chips, yet with performance that tracks an ASIC more closely than an FPGA. This paper examines the architectural design choices in this chip-design system. These choices include the definition of reasonable bricks, both in functionality and size, as well as the communication interconnect that the I/O cap provides. To do this we synthesize candidate bricks, analyze their area and bandwidth demands, and present an architectural design for the inter-brick communication network. We discuss a sample chip design, a 16-way CMP, and analyze the costs and benefits of designing chips with brick and mortar. We find that this method of producing chips incurs only a small performance loss (8%) compared to a fully custom ASIC, which is significantly less than the degradation seen from other low-overhead chip options, such as FPGAs. Finally, we measure the effect that architectural design decisions have on the behavior of the proposed physical brick assembly technique, fluidic self-assembly.