We present a deep Blanco/DECam colour-magnitude diagram (CMD) for the large but very diffuse Milky Way satellite dwarf galaxy Crater II. The CMD shows only old stars with a clearly bifurcated subgiant branch (SGB) that feeds a narrow red giant branch. The horizontal branch (HB) shows many RR Lyrae and red HB stars. Comparing the CMD with [Fe/H] = -2.0 and [alpha/Fe]=+ 0.3 alpha-enhanced BaSTI isochrones indicates a mean age of 12.5Gyr for the main event and a mean age of 10.5Gyr for the brighter SGB. With such multiple star formation events Crater II shows similarity to more massive dwarfs that have intermediate age populations, however for Crater II there was early quenching of the star formation and no intermediate age or younger stars are present. The spatial distribution of Crater II stars overall is elliptical in the plane of the sky, the detailed distribution shows a lack of strong central concentration, and some inhomogeneities. The 10.5Gyr subgiant and upper main-sequence stars show a slightly higher central concentration when compared to the 12.5Gyr population. Matching to Gaia DR2 we find the proper motion of Crater II: mu alpha(cos) delta =-0.14 +/- 0.07, mu(delta) = -0.10 +/- 0.04 mas yr(-1), approximately perpendicular to the semimajor axis of Crater II. Our results provide constraints on the star formation and chemical enrichment history of Crater II, but cannot definitively determine whether or not substantial mass has been lost over its lifetime.