  We present the Obelisk project, a cosmological radiation-hydrodynamics
simulation following the assembly and reionization of a protocluster progenitor
during the first two billions of years from the big bang, down to $z = 3.5$.
The simulation resolves haloes down to the atomic cooling limit, and tracks the
contribution of different sources of ionization: stars, active galactic nuclei,
and collisions. The Obelisk project is designed specifically to study the
coevolution of high redshift galaxies and quasars in an environment favouring
black hole growth. In this paper, we establish the relative contribution of
these two sources of radiation to reionization and their respective role in
establishing and maintaining the high redshift ionizing background. Our volume
is typical of an overdense region of the Universe and displays star formation
rate and black hole accretion rate densities similar to high redshift
protoclusters. We find that hydrogen reionization happens inside-out and is
completed by $z \sim 6$ in our overdensity, and is predominantly driven by
galaxies, while accreting black holes only play a role at $z \sim 4$.
