  We investigate the vortex phase diagram in untwinned YBaCuO single crystals
with columnar defects. These randomly distributed defects, produced by heavy
ion irradiation, are expected to induce a ``Bose Glass'' phase of localized
vortices characterized by a vanishing resistance and a Meissner effect for
magnetic fields transverse to the defect axis. We directly observe the
transverse Meissner effect using an array of Hall probe magnetometers. As
predicted, the Meissner state breaks down at temperatures Ts that decrease
linearly with increasing transverse magnetic field. However, Ts falls well
below the conventional melting temperature Tm determined by a vanishing
resistivity, suggesting an intermediate regime where flux lines are effectively
localized even when rotated off the columnar defects.
