We study the phase diagram of a strongly coupled confining theory in 2+1 dimensions, as a function of temperature and baryon chemical potential. The theory has a fully fledged supergravity holographic dual, that we use to predict a line of first-order phase transitions separating a confining phase and a deconfined phase. Both phases exhibit a nonzero baryon density thus providing a first example of baryonic matter in a confining string dual that does not require the introduction of flavor branes. We argue that the confining phase is a baryon superfluid, while the deconfined phase has nonzero baryon magnetization.