Recent observations of the high-mass X-ray binary Cygnus X-1 have shown that both the companion star (41 solar masses) and the black hole (21 solar masses) are more massive than previously estimated. Furthermore, the black hole appears to be nearly maximally spinning. Here, we present a possible formation channel for the Cygnus X-1 system that matches the observed system properties. In this formation channel, we find that the orbital parameters of Cygnus X-1, combined with the observed metallicity of the companion, imply a significant reduction in mass loss through winds relative to commonly used prescriptions for stripped stars.