  Our understanding of various states of matter usually relies on the
assumption of thermodynamic equilibrium. However, the transitions between
different phases of matter can be strongly affected by non-equilibrium
phenomena. Here we demonstrate and explain an example of non-equilibrium
stalling of a continuous, second-order phase transition. We create a
superheated atomic Bose gas, in which a Bose-Einstein condensate (BEC) persists
above the equilibrium critical temperature, $T_c$, if its coupling to the
surrounding thermal bath is reduced by tuning interatomic interactions. For
vanishing interactions the BEC persists in the superheated regime for a minute.
However, if strong interactions are suddenly turned on, it rapidly "boils"
away. Our observations can be understood within a two-fluid picture, treating
the condensed and thermal components of the gas as separate equilibrium systems
with a tuneable inter-component coupling. We experimentally reconstruct a
non-equilibrium phase diagram of our gas, and theoretically reproduce its main
features.
