  We use archival Chandra X-ray Observatory data to investigate X-ray emission
from early-type galaxies in the rich z=0.06 cluster Abell 3128. By combining
the X-ray count-rates from an input list of optically-selected galaxies, we
obtain a statistical detection of X-ray flux, unbiased by X-ray selection
limits. Using 87 galaxies with reliable Chandra data, X-ray emission is
detected for galaxies down to M_B ~ -19.0, with only an upper limit determined
for galaxies at M_B ~ -18.3. The ratio of X-ray to optical luminosities is
consistent with recent determinations of the low-mass X-ray binary content of
nearby elliptical galaxies. Taken individually, in contrast, we detect
significant (3sigma) flux for only six galaxies. Of these, one is a foreground
galaxy, while two are optically-faint galaxies with X-ray hardness ratios
characteristic of active galactic nuclei. The remaining three detected galaxies
are amongst the optically-brightest cluster members, and have softer X-ray
spectra. Their X-ray flux is higher than that expected from X-ray binaries, by
a factor 2-10; the excess suggests these galaxies have retained their hot
gaseous haloes. The source with the highest L_X / L_B ratio is of unusual
optical morphology with prominent sharp-edged shells. Notwithstanding these few
exceptions, the cluster population overall exhibits X-ray properties consistent
with their emission being dominated by X-ray binaries. We conclude that in rich
cluster environments, interaction with the ambient intra-cluster medium acts to
strip most galaxies of their hot halo gas.
