  We report on a Monte Carlo study of a diluted Ising antiferromagnet on a fcc
lattice. This is a typical model example of a highly frustrated
antiferromagnet, and we ask, whether sufficient random dilution of spins does
produce a spin glass phase. Our data strongly indicate the existence of a spin
glass transition for spin--concentration $p<0.75$: We find a divergent spin
glass susceptibility and a divergent spin glass correlation length, whereas the
antiferromagnetic correlation length saturates in this regime. Furthermore, we
find a first order phase transition to an antiferromagnet for $1\ge p>0.85$,
which becomes continuous in the range $0.85>p>0.75$. Finite size scaling is
employed to obtain critical exponents. We compare our results with experimental
systems as diluted frustrated antiferromagnets as ${\rm Zn_{1-p}Mn_{p}Te}$.
