  Via extensive Monte Carlo studies we show that the frustrated XY Hamiltonian
on a 2-D Penrose lattice admits of a spin glass phase at low temperature.
Studies of the Edwards-Anderson order parameter, spin glass susceptibility, and
local (linear) susceptibility point unequivocally to a paramagnetic to spin
glass transition as the temperature is lowered. Specific heat shows a rounded
peak at a temperature above the spin glass transition temperature, as is
commonly observed in spin glasses. Our results strongly suggest that the
critical point exponents are the same as obtained by Bhatt and Young in the
${\pm}J$ Ising model on a square lattice. However, unlike in the latter case,
the critical temperature is clearly finite (nonzero). The results imply that a
quasiperiodic 2-D array of superconducting grains in a suitably chosen
transverse magnetic field should behave as a superconducting glass at low
temperature.
