We report the discovery of a new ultra-short period transiting hot Jupiter from the Next Generation Transit Survey (NGTS). NGTS-10b has a mass and radius of $2.162-0.107+0.092$ M and $1.205-0.083+0.117$ R and orbits its host star with a period of $0.7668944\pm 0.0000003$ days, making it the shortest period hot Jupiter yet discovered. The host is a $10.4\pm 2.5$ Gyr old K5V star ($T\mathrm{eff}$=$4400\pm 100$,K) of Solar metallicity ([Fe/H] = $-0.02\pm 0.12$,dex) showing moderate signs of stellar activity. NGTS-10b joins a short list of ultra-short period Jupiters that are prime candidates for the study of star-planet tidal interactions. NGTS-10b orbits its host at just $1.46\pm 0.18$ Roche radii, and we calculate a median remaining inspiral time of $38$,Myr and a potentially measurable transit time shift of $7$,seconds over the coming decade, assuming a stellar tidal quality factor $Qs\prime =2\times 107$.