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NASA is extending human exploration of space beyond the low earth orbit and moon to Mars. To save cost, it has been determined that In Situ Propellant Production (ISPP) is a key enabling technology in Mission to Mars. A cryocooler is needed to liquefy and store oxygen and methane on the Mars surface. In an earlier study by the authors, a single-stage reverse Brayton cycle cryocooler was proposed with neon as the working fluid. The cryocooler operates between 80K and 310K. It was shown that a highly effective recuperative heat exchanger is vital to the overall efficiency of the cryogenic system. To achieve a COP of 0.2 or better, the heat exchanger should have an effectiveness of 0.97 or better while the percentage pressure drop should be less than 3%. In this paper, the design and analysis of a highly effective micro heat exchanger is presented. The heat exchanger is a multi-layer pile of parallel square ducts. The cold and hot fluids flow in a counter flow manner.