ABSTRACT While low-luminosity galaxies dominate number counts at all redshifts, their contribution to cosmic reionization is poorly understood due to a lack of knowledge of their physical properties. We isolate a sample of 35 z ≈ 4–5 continuum-faint Lyman-α emitters from deep VLT/MUSE spectroscopy and directly measure their H α emission using stacked Spitzer/IRAC Ch. 1 photometry. Based on Hubble Space Telescope imaging, we determine that the average UV continuum magnitude is fainter than −16 (≈ 0.01 L⋆), implying a median Lyman-α equivalent width of 259 Å. By combining the H α measurement with the UV magnitude, we determine the ionizing photon production efficiency, ξion, a first for such faint galaxies. The measurement of log10 (ξion [Hz erg−1]) = 26.28 ($^{+0.28}_{-0.40}$) is in excess of literature measurements of both continuum- and emission line-selected samples, implying a more efficient production of ionizing photons in these lower luminosity, Lyman-α-selected systems. We conclude that this elevated efficiency can be explained by stellar populations with metallicities between 4 × 10−4 and 0.008, with light-weighted ages less than 3 Myr.