The pervaporation of chloroform-water solutions across polysulfone hollow fibers thinly coated with polydimethylsiloxane (PDMS) is largely controlled by mass transfer in the feed. The mass transfer coefficients in the feed agree closely with literature correlations for cross flow on the shell side of baffled modules. They do not agree with literature correlations for lumen flow, probably because the flows here are at Reynolds numbers in the transition region. The mass transfer resistance of the coated fiber itself is consistent with the known properties of PDMS. The mass transfer resistances on the permeate side are negligible.