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The fission Time Projection Chamber (fissionTPC) is a compact (15 cm diameter) two-chamber MICROMEGAS TPC designed to make precision cross section measurements of neutron-induced fission. The actinide targets are placed on the central cathode and irradiated with a neutron beam that passes axially through the TPC inducing fission in the target. The 4π acceptance for fission fragments and complete charged particle track reconstruction are powerful features of the fissionTPC which will be used to measure fission cross sections and examine the associated systematic errors. This paper provides a detailed description of the design requirements, the design solutions, and the initial performance of the fissionTPC.