We find the angular diameter of R Doradus to be 57 +/- 5 mas, exceeding that of Betelgeuse and implying that R Dor is larger in apparent size than every star except the Sun. R Dor is shown to be closely related to the Mira variables. We estimate an effective temperature of 2740 +/- 190 K, a distance of 61 +/- 7 pc, a luminosity of 6500 +/- 1400 Lsol and a radius of 370 +/- 50 Rsol. The characteristics of R Dor are consistent with it being near the edge of a Mira instability strip. We detect non-zero closure phases from R Dor, indicating an asymmetric brightness distribution. We also observed W Hya, a small-amplitude Mira, for which we find an angular diameter of 44 +/- 4 mas.