We report the detection of a transiting super-Earth-sized planet (R = 1.39 ± 0.09 R_⊕) in a 1.4-day orbit around L 168-9 (TOI-134), a bright M1V dwarf (V = 11, K = 7.1) located at 25.15 ± 0.02 pc. The host star was observed in the first sector of the Transiting Exoplanet Survey Satellite (TESS) mission. For confirmation and planet mass measurement purposes, this was followed up with ground-based photometry, seeing-limited and high-resolution imaging, and precise radial velocity (PRV) observations using the HARPS and Magellan/PFS spectrographs. By combining the TESS data and PRV observations, we find the mass of L 168-9 b to be 4.60 ± 0.56 M_⊕ and thus the bulk density to be 1.74_−0.33^+0.44 times higher than that of the Earth. The orbital eccentricity is smaller than 0.21 (95% confidence). This planet is a level one candidate for the TESS mission’s scientific objective of measuring the masses of 50 small planets, and it is one of the most observationally accessible terrestrial planets for future atmospheric characterization.