<p>We study the dynamics of a first-order phase transition in a strongly coupled gauge theory at non-zero temperature and chemical potential, computing nucleation rates and wall speeds from first principles. The gauge theory is the four-dimensional superconformal SU(<i>N</i>) × SU(<i>N</i>) Klebanov-Witten theory, which at low temperatures displays an instability to forming scalar condensates that higgses the theory. The computation is made possible by utilizing the gravity dual, type IIB string theory on asymptotically AdS₅ × <i>T</i>^1<i>,</i>1 spacetimes. The instability is detected through the nucleation and subsequent localization of D-branes in the bulk, which in the probe limit is amenable to calculations. The nucleation rates suggest a preference for greater asymmetry between the two gauge groups as the temperature is lowered beyond its critical value. The wall speed stays below the speed of sound of the conformal plasma across all parameter values and exhibits nonlinear dependence on the energy difference between the two phases.</p>