  We report the discovery of TOI-561, a multi-planet system in the galactic
thick disk that contains a rocky, ultra-short period planet (USP). This bright
($V=10.2$) star hosts three small transiting planets identified in photometry
from the NASA TESS mission: TOI-561 b (TOI-561.02, P=0.44 days, $R_b =
1.45\pm0.11\,R_\oplus$), c (TOI-561.01, P=10.8 days,
$R_c=2.90\pm0.13\,R_\oplus$), and d (TOI-561.03, P=16.3 days,
$R_d=2.32\pm0.16\,R_\oplus$). The star is chemically ([Fe/H]$=-0.41\pm0.05$,
[$\alpha$/H]$=+0.23\pm0.05$) and kinematically consistent with the galactic
thick disk population, making TOI-561 one of the oldest ($10\pm3\,$Gyr) and
most metal-poor planetary systems discovered yet. We dynamically confirm
planets b and c with radial velocities from the W. M. Keck Observatory High
Resolution Echelle Spectrometer. Planet b has a mass and density of
$3.2\pm0.8\,M_\oplus$ and $5.5^{+2.0}_{-1.6}\,$g$\,$cm$^{-3}$, consistent with
a rocky composition. Its lower-than-average density is consistent with an
iron-poor composition, although an Earth-like iron-to-silicates ratio is not
ruled out. Planet c is $7.0\pm2.3\,M_\oplus$ and $1.6\pm0.6\,$g$\,$cm$^{-3}$,
consistent with an interior rocky core overlaid with a low-mass volatile
envelope. Several attributes of the photometry for planet d (which we did not
detect dynamically) complicate the analysis, but we vet the planet with
high-contrast imaging, ground-based photometric follow-up and radial
velocities. TOI-561 b is the first rocky world around a galactic thick-disk
star confirmed with radial velocities and one of the best rocky planets for
thermal emission studies.
