  We formulate the field equations for $SU(\infty)$ Einstein-Yang-Mills theory,
and find spherically symmetric black-hole solutions. This model may be
motivated by string theory considerations, given the enormous gauge symmetries
which characterize string theory. The solutions simplify considerably in the
presence of a negative cosmological constant, particularly for the limiting
cases of a very large cosmological constant or very small gauge field. The
situation of an arbitrarily small gauge field is relevant for holography and we
comment on the AdS/CFT conjecture in this light. The black holes possess
infinite amounts of gauge field hair, and we speculate on possible consequences
of this for quantum decoherence, which, however, we do not tackle here.
