© 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. We introduce redMaGiC, an automated algorithm for selecting luminous red galaxies (LRGs). The algorithm was specifically developed to minimize photometric redshift uncertainties in photometric large-scale structure studies. redMaGiC achieves this by self-training the colour cuts necessary to produce a luminosity-thresholded LRG sample of constant comoving density. We demonstrate that redMaGiC photo-zs are very nearly as accurate as the best machine learning-based methods, yet they require minimal spectroscopic training, do not suffer from extrapolation biases, and are very nearly Gaussian. We apply our algorithm to Dark Energy Survey (DES) Science Verification (SV) data to produce a redMaGiC catalogue sampling the redshift range z ∈ [0.2, 0.8]. Our fiducial sample has a comoving space density of 10-3 (h-1 Mpc)-3, and a median photo-z bias (zspec - zphoto) and scatter (σz/(1 + z)) of 0.005 and 0.017, respectively. The corresponding 5σ outlier fraction is 1.4 per cent. We also test our algorithm with Sloan Digital Sky Survey Data Release 8 and Stripe 82 data, and discuss how spectroscopic training can be used to control photo-z biases at the 0.1 per cent level.