The present invention is a low haze thermoplastic polyurethane (TPU) comprising structural units of a diisocyanate; a diol and three different chain extenders (butanediol chain extender; a different linear diol co-chain-extender and a cyclic co-chain-ex-tender). The TPU has good combinations of light transmission and clarity, low temperature flexibility, and high moisture vapor transition rates compared to other commercial or known TPUs. The preferred composition is a TPU that is based on polycaprolactone as diol, MDI as the diisocyanate monomer, butanediol chain extender, 1,3 propanediol linear chain co-extender and cyclohexanedimethanol cyclic chain co-extenders, and has good clarity and tensile strength.