  The extreme environments of ultra-short-period planets (USPs) make excellent
laboratories to study how exoplanets obtain, lose, retain, and/or regain
gaseous atmospheres. We present the confirmation and characterization of the
USP TOI-1347 b, a $1.8 \pm 0.1$ R$_\oplus$ planet on a 0.85 day orbit that was
detected with photometry from the TESS mission. We measured radial velocities
of the TOI-1347 system using Keck/HIRES and HARPS-N and found the USP to be
unusually massive at $11.1 \pm 1.2$ M$_\oplus$. The measured mass and radius of
TOI-1347 b imply an Earth-like bulk composition. A thin H/He envelope (>0.01%
by mass) can be ruled out at high confidence. The system is between 1 and 1.8
Gyr old; therefore, intensive photoevaporation should have concluded. We
detected a tentative phase curve variation (3$\sigma$) and a secondary eclipse
(2$\sigma$) in TESS photometry, which if confirmed could indicate the presence
of a high-mean-molecular-weight atmosphere. We recommend additional optical and
infrared observations to confirm the presence of an atmosphere and investigate
its composition.
