  (Abridged) We present the results of photometric measurements from images of
the LMC globular clusters NGC 1928, 1939 and Reticulum taken with ACS on HST.
F555W and F814W exposures result in high accuracy CMDs for these three
clusters. This is the first time that CMDs for NGC 1928 and 1939 have been
published. All three clusters possess CMDs with features indicating them to be
>10 Gyr old, including main sequence turn-offs at V~23 and well populated HBs.
We use the CMDs to obtain metallicity and reddening estimates for each cluster.
NGC 1939 is a metal poor cluster, with [Fe/H] = -2.10 +/- 0.19, while NGC 1928
is significantly more metal rich, with [Fe/H] = -1.27 +/- 0.14. Reticulum's
abundance lies between the two, at [Fe/H] = -1.66 +/- 0.12. All three clusters
are moderately reddened with values ranging from E(V-I) = 0.07 +/- 0.02 for
Reticulum and E(V-I) = 0.08 +/- 0.02 for NGC 1928, to E(V-I) = 0.16 +/- 0.03
for NGC 1939. We estimate the HB morphology of each cluster. NGC 1928 and 1939
possess HBs consisting almost exclusively of stars to the blue of the
instability strip. In contrast, Reticulum has an intermediate HB morphology,
with stars across the instability strip. Using a variety of dating techniques
we show that these three clusters are coeval with each other and the oldest
Galactic and LMC globular clusters, to within ~2 Gyr. The census of known old
LMC globular clusters therefore now numbers 15 plus the unique, somewhat
younger cluster ESO121-SC03. The NGC 1939 field contains another cluster in the
line-of-sight, NGC 1938. A CMD for this object shows it to be less than ~400
Myr old, and it is therefore unlikely to be physically associated with NGC
1939.
