A hollow fiber carbon molecular sieve membrane, a process for preparing the hollow fiber carbon molecular sieve membrane, and a process for effecting separation of an olefin from a gaseous mixture that comprises the olefin in admixture with its corresponding paraffin and optionally one or more gaseous components selected from hydrogen, an olefin other than the olefin and a paraffin other than the corresponding paraffin. The process and membrane may also be used to effect separation of the olefin(s) from remaining feedstream components subsequent to an olefin-paraffin separation.