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. One-dimensional and three-dimensional numerical models were used to aid in the design. It was determined that in order to achieve an overall pressure drop of 3% or less, the system pressure should be at 4 bars or higher. The need to reduce axial wall conduction to an acceptable level suggests that the heat exchanger should utilize thin wall ducts (20 microns thick) and be constructed with materials with low thermal conductivity (silicon dioxide). The optimal dimensions of the duct are 100 microns for the duct width and 83 mm for the length of the duct.