GPU and FPGA-based clouds have already demonstrated the promise of accelerating computing-intensive workloads with greatly improved power and performance. In this paper, we examine the design of ASIC Clouds, which are purpose-built datacenters comprised of large arrays of ASIC accelerators, whose purpose is to optimize the total cost of ownership (TCO) of large, high-volume chronic computations, which are becoming increasingly common as more and more services are built around the Cloud model. On the surface, the creation of ASIC clouds may seem highly improbable due to high NREs and the inflexibility of ASICs. Surprisingly, however, large-scale ASIC Clouds have already been deployed by a large number of commercial entities, to implement the distributed Bitcoin cryptocurrency system. We begin with a case study of Bitcoin mining ASIC Clouds, which are perhaps the largest ASIC Clouds to date. From there, we design three more ASIC Clouds, including a YouTube-style video transcoding ASIC Cloud, a Litecoin ASIC Cloud, and a Convolutional Neural Network ASIC Cloud and show 2-3 orders of magnitude better TCO versus CPU and GPU. Among our contributions, we present a methodology that given an accelerator design, derives Pareto-optimal ASIC Cloud Servers, by extracting data from place-and-routed circuits and computational fluid dynamic simulations, and then employing clever but brute-force search to find the best jointly-optimized ASIC, DRAM subsystem, motherboard, power delivery system, cooling system, operating voltage, and case design. Moreover, we show how data center parameters determine which of the many Pareto-optimal points is TCO-optimal. Finally we examine when it makes sense to build an ASIC Cloud, and examine the impact of ASIC NRE.