  The extragalactic X-ray binary IC 10 X-1 has attracted attention as it is
possibly the host of the most massive stellar-mass black-hole (BH) known to
date. Here we consider all available observational constraints and construct
its evolutionary history up to the instant just before the formation of the BH.
Our analysis accounts for the simplest possible history that includes three
evolutionary phases: binary orbital dynamics at core collapse, common envelope
(CE) evolution, and evolution of the BH--helium star binary progenitor of the
observed system. We derive the complete set of constraints on the progenitor
system at various evolutionary stages. Specifically: right before the core
collapse event, we find the mass of the BH immediate progenitor to be > 31 Msun
(at 95% of confidence, same hereafter). The magnitude of the natal kick
imparted to the BH is constrained to be < 130 km/s. Furthermore, we find that
the "enthalpy" formalism recently suggested by Ivanova & Chaichenets is able to
explain the existence of IC 10 X-1 without the need of invoking unreasonably
high CE efficiencies. With this physically motivated formalism, we find that
the CE efficiency required to explain the system is in the range of 0.6--1.
