We report the first discovery of a thick-disk planet, LHS 1815b (TOI-704b, TIC 260004324), detected in the Transiting Exoplanet Survey Satellite (TESS) survey. LHS 1815b transits a bright (V = 12.19 mag, K = 7.99 mag) and quiet M dwarf located 29.87 ± 0.02 pc away with a mass of 0.502 ± 0.015 M☉ and a radius of 0.501 ± 0.030 R☉. We validate the planet by combining space- and ground-based photometry, spectroscopy, and imaging. The planet has a radius of 1.088 ± 0.064 R⊕ with a 3σ mass upper limit of 8.7 M⊕. We analyze the galactic kinematics and orbit of the host star LHS 1815 and find that it has a large probability (Pthick/Pthin = 6482) to be in the thick disk with a much higher expected maximal height (Zmax = 1.8 kpc) above the Galactic plane compared with other TESS planet host stars. Future studies of the interior structure and atmospheric properties of planets in such systems using, for example, the upcoming James Webb Space Telescope, can investigate the differences in formation efficiency and evolution for planetary systems between different Galactic components (thick disks, thin disks, and halo).