  Ultra-short-period (USP) exoplanets have orbital periods shorter than one
day. Precise masses and radii of USPs could provide constraints on their
unknown formation and evolution processes. We report the detection and
characterization of the USP planet GJ 367b using high precision photometry and
radial velocity observations. GJ 367b orbits a bright (V-band magnitude =
10.2), nearby, red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of
$0.718 \pm 0.054$ Earth-radii, a mass of $0.546 \pm 0.078$ Earth-masses, making
it a sub-Earth. The corresponding bulk density is $8.106 \pm 2.165$ g cm$^-3$,
close to that of iron. An interior structure model predicts the planet has an
iron core radius fraction of $86 \pm 5\%$, similar to Mercury's interior.
