We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). The key lies in relating standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutations in the system of identical bosons --- is crucial in either case. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality. As a byproduct, we obtain a characterization of the partially-confined/partially-deconfined phase at finite coupling: the constant offset of the distribution of the phases of the Polyakov loop is the order parameter.