  Strongly correlated systems can exhibit surprising phenomena when brought in
a state far from equilibrium. A spectacular example are quantum avalanches,
that have been predicted to run through a many-body--localized system and
delocalize it. Quantum avalanches occur when the system is locally coupled to a
small thermal inclusion that acts as a bath. Here we realize an interface
between a many-body--localized system and a thermal inclusion of variable size,
and study its dynamics. We find evidence for accelerated transport into the
localized region, signature of a quantum avalanche. By measuring the
site-resolved entropy we monitor how the avalanche travels through the
localized system and thermalizes it site by site. Furthermore, we isolate the
bath-induced dynamics by evaluating multipoint correlations between the bath
and the system. Our results have fundamental implications on the robustness of
many-body--localized systems and their critical behavior.
