We report on HST observations of six candidate old globular clusters in the Large Magellanic Cloud: NGC 1754, NGC 1835, NGC 1898, NGC 1916, NGC 2005 and NGC 2019. Deep exposures with the F555W and F814W filters provide us with colourmagnitude diagrams that reach to an apparent magnitude in V of ∼25, well below the main sequence turnoff. These particular clusters are involved with significantly high LMC field star densities and care was taken to subtract the field stars from the cluster colour-magnitude diagrams accurately. In two cases there is significant variable reddening across at least part of the image, but only for NGC 1916 does the differential reddening preclude accurate measurements of the CMD characteristics. The morphologies of the colour-magnitude diagrams match well those of Galactic globular clusters of similar metallicity. All six have well-developed horizontal branches, while four clearly have stars on both sides of the RR Lyrae gap. The abundances obtained from measurements of the height of the red giant branch above the level of the horizontal branch are 0.3 dex higher, on average, than previously measured spectroscopic abundances. Detailed comparisons with Galactic globular cluster fiducials show that all six clusters are old objects, very similar in age to classical Galactic globulars such as M5, with little age spread among the clusters. This result is consistent with ages derived by measuring the magnitude difference between the horizontal branch and main sequence turnoff. We also find a similar chronology by comparing the horizontal branch morphologies and abundances with the horizontal branch evolutionary tracks of Lee, Demarque, & Zinn (1994). Our results imply that the LMC formed at the same time as the Milky Way Galaxy.