  Hot Jupiters are rarely accompanied by other planets within a factor of a few
in orbital distance. Previously, only two such systems have been found. Here,
we report the discovery of a third system using data from the Transiting
Exoplanet Survey Satellite (TESS). The host star, TOI-1130, is an 11th
magnitude K-dwarf in the Gaia G band. It has two transiting planets: a
Neptune-sized planet ($3.65\pm 0.10$ $R_E$) with a 4.1-day period, and a hot
Jupiter ($1.50^{+0.27}_{-0.22}$ $R_J$) with an 8.4-day period. Precise
radial-velocity observations show that the mass of the hot Jupiter is
$0.974^{+0.043}_{-0.044}$ $M_J$. For the inner Neptune, the data provide only
an upper limit on the mass of 0.17 $M_J$ (3$\sigma$). Nevertheless, we are
confident the inner planet is real, based on follow-up ground-based photometry
and adaptive optics imaging that rule out other plausible sources of the TESS
transit signal. The unusual planetary architecture of and the brightness of the
host star make TOI-1130 a good test case for planet formation theories, and an
attractive target for future spectroscopic observations.
