NGTS-10b: The shortest period hot Jupiter yet discovered.

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 $2.162\,^{+0.092}_{-0.107}$ M$_{\rm J}$ and $1.205\,^{+0.117}_{-0.083}$ R$_{\rm J}$ and orbits its host star with a period of $0.7668944\pm0.0000003$ days, making it the shortest period hot Jupiter yet discovered. The host is a $10.4\pm2.5$ Gyr old K5V star ($T_\mathrm{eff}$=$4400\pm100$\,K) of Solar metallicity ([Fe/H] = $-0.02\pm0.12$\,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 $1.46\pm0.18$ 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 $Q'_{\rm s}=2\times10^{7}$.