  Cosmological phase transitions proceed via the nucleation of bubbles that
subsequently expand and collide. The resulting gravitational wave spectrum
depends crucially on the bubble wall velocity. Microscopic calculations of this
velocity are challenging even in weakly coupled theories. We use holography to
compute the wall velocity from first principles in a strongly coupled,
non-Abelian, four-dimensional gauge theory. The wall velocity is determined
dynamically in terms of the nucleation temperature. We find an approximately
linear relation between the velocity and the ratio $\Delta
\mathcal{P}/\mathcal{E}$, with $\Delta \mathcal{P}$ the pressure difference
between the inside and the outside of the bubble and $\mathcal{E}$ the energy
density outside the bubble. Up to a rescaling, the wall profile is well
approximated by that of an equilibrium, phase-separated configuration at the
critical temperature. We verify that ideal hydrodynamics provides a good
description of the system everywhere except near the wall.
