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, $R_b = 1.45pm0.11,R_oplus$), c (TOI-561.01, P=10.8 days, $R_c=2.90pm0.13,R_oplus$), and d (TOI-561.03, P=16.3 days, $R_d=2.32pm0.16,R_oplus$). The star is chemically ([Fe/H]$=-0.41pm0.05$, [$alpha$/H]$=+0.23pm0.05$) and kinematically consistent with the galactic thick disk population, making TOI-561 one of the oldest ($10pm3,$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 $3.2pm0.8,M_oplus$ 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 $7.0pm2.3,M_oplus$ and $1.6pm0.6,$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.
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