  We pioneer the black hole mass gap as a powerful new tool for constraining
modified gravity theories. These theories predict fifth forces that alter the
structure and evolution of population-III stars, exacerbating the
pair-instability. This results in the formation of lighter astrophysical black
holes and lowers both the upper and lower edges of the mass gap. These effects
are explored using detailed numerical simulations to derive quantitative
predictions that can be used as theoretical inputs for Bayesian data analysis.
We discuss detection strategies in light of current and upcoming data as well
as complications that may arise due to environmental screening. To demonstrate
the constraining power of the mass gap, we present a novel test of the strong
equivalence principle where we apply our results to an analysis of the first
ten LIGO/Virgo binary black hole merger events to obtain a $7\%$ bound on the
relative difference between the gravitational constant experienced by baryonic
matter, and that experienced by black holes, $\Delta G/G$. The recent GW190521
event resulting from two black holes with masses in the canonical mass gap can
be explained by modified gravity if the event originated from an unscreened
galaxy where the strength of gravity is enhanced by $\sim30\%$ or reduced by
$\sim 50\%$ relative to its strength in the solar system.
