Diffraction gratings have simplified the optical implementation of magneto-optical traps (MOTs) to require only a single input beam, however reaching high atom number and fast loading has proven to be a challenge. We equipped an atom chip with a grating surface and paired it with a velocity-tunable 2D+-MOT as an atomic source to facilitate efficient loading together with magnetic trapping. Using uniform grating illumination, we magneto-optically trap 1.0(1)×109 atoms within one second, cool them to 14.1(3)μK, and transfer a quarter of them into the magnetic chip trap. This is a key step towards simple portable quantum sensors employing (ultra-)cold atoms.