The difficulties in reconciling gravity with quantum mechanics are nowhere better illustrated than in the cosmological or vacuum dark energy that recent observations suggest pervade the whole universe, causing its expansion to accelerate; and black holes, the final state of complete gravitational collapse of matter into a singularity of space and time. After reviewing the problems that arise when attempting to bring these two phenomena into accordance with quantum principles, I propose that the cosmological vacuum may be regarded as a new kind of gravitational Bose-Einstein condensate (GBEC). If this GBEC state can be produced in a quantum phase transition during the gravitational collapse process, then a new kind of cold, compact object called a Gravitational Condensate Star can form. Unlike a black hole of classical general relativity, a collapsed star of this kind has no singularities, no event horizon, no information paradox and is thermodynamically stable. Some possible observational consequences of this hypothesis will be discussed.