Homochiral membrane bilayers organize biological functions in all domains of life. The membrane's permeability-its key property-correlates with a molecule's lipophilicity, but the role of the membrane's rich and uniform stereochemistry as a permeability determinant is largely ignored in empirical and computational measurements. Here, we describe a new approach to measuring permeation using continuously generated microfluidic droplet interface bilayers (DIBs, generated at a rate of 480 per minute) and benchmark this system by monitoring fluorescent dye DIB permeation over time. Enantioselective permeation of alkyne-labelled amino acids (Ala, Val, Phe, Pro) and dipeptides through a chiral phospholipid bilayer was demonstrated using DIB transport measurements; the biological L enantiomers permeated faster than the D enantiomers (from 1.2-fold to 6-fold for Ala to Pro). Enantioselective permeation both poses a potentially unanticipated criterion for drug design and offers a kinetic mechanism for the abiotic emergence of homochirality via chiral transfer between sugars, amino acids and lipids.