Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects $10^7$ $^{87}$Rb atoms, which are subsequently cooled to $20,mu$K in optical molasses. We optically probe the microwave atomic ground-state splitting using lin$perp$lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only $0.5,$mm, the measured short-term fractional frequency stability is $2 times 10 ^{-11} /sqrt{tau}$.
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