  We present the TESS discovery of the LHS 1678 (TOI-696) exoplanet system,
comprised of two approximately Earth-sized transiting planets and a likely
astrometric brown dwarf orbiting a bright ($V_J$=12.5, $K_s$=8.3) M2 dwarf at
19.9 pc. The two TESS-detected planets are of radius 0.70$\pm$0.04 $R_\oplus$
and 0.98$\pm$0.06 $R_\oplus$ in 0.86-day and 3.69-day orbits, respectively.
Both planets are validated and characterized via ground-based follow-up
observations. HARPS RV monitoring yields 97.7 percentile mass upper limits of
0.35 $M_\oplus$ and 1.4 $M_\oplus$ for planets b and c, respectively. The
astrometric companion detected by the CTIO/SMARTS 0.9m has an orbital period on
the order of decades and is undetected by other means. Additional ground-based
observations constrain the companion to being a high-mass brown dwarf or
smaller. Each planet is of unique interest; the inner planet has an ultra-short
period, and the outer planet is in the Venus zone. Both are promising targets
for atmospheric characterization with the JWST and mass measurements via
extreme-precision radial velocity. A third planet candidate of radius
0.9$\pm$0.1 $R_\oplus$ in a 4.97-day orbit is also identified in multi-Cycle
TESS data for validation in future work. The host star is associated with an
observed gap in the lower main sequence of the Hertzsprung-Russell diagram.
This gap is tied to the transition from partially- to fully-convective
interiors in M dwarfs, and the effect of the associated stellar astrophysics on
exoplanet evolution is currently unknown. The culmination of these system
properties makes LHS 1678 a unique, compelling playground for comparative
exoplanet science and understanding the formation and evolution of small,
short-period exoplanets orbiting low-mass stars.
