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 eleventh magnitude K-dwarf in Gaia G-band. It has two transiting planets: a Neptune-sized planet (3.65 ± 0.10 R_{\oplus }) with a 4.1 days period, and a hot Jupiter ({1.50}_{-0.22}^{+0.27} R_{J}) with an 8.4 days period. Precise radial-velocity observations show that the mass of the hot Jupiter is {0.974}_{-0.044}^{+0.043} M_{J}. For the inner Neptune, the data provide only an upper limit on the mass of 0.17 M_{J} (3σ). Nevertheless, we are confident that 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.