We present the results of photometric measurements from images of the LMC globular clusters NGC 1928 , 1939 and Reticulum taken with the Advanced Camera for Surveys on the Hubble Space Telescope . Exposures through the F555W and F814W filters result in high accuracy colour-magnitude diagrams ( 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 \sim 23 and well populated horizontal branches ( 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 \pm 0.19 , while NGC 1928 is significantly more metal-rich , with [ { Fe } / { H } ] = -1.27 \pm 0.14 . The abundance of Reticulum is intermediate between the two , with [ { Fe } / { H } ] = -1.66 \pm 0.12 – a measurement which matches well with previous estimates . All three clusters are moderately reddened , with values ranging from E ( V - I ) = 0.07 \pm 0.02 for Reticulum and E ( V - I ) = 0.08 \pm 0.02 for NGC 1928 , to E ( V - I ) = 0.16 \pm 0.03 for NGC 1939 . After correcting the CMDs for extinction 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 , with NGC 1928 in addition showing evidence for an extended blue HB . 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 \sim 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 \sim 400 Myr old , and it is therefore unlikely to be physically associated with NGC 1939 .