(ProQuest: ... denotes formulae and/or non-USASCII text omitted)We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly understood but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 (EPIC 206247743) is an evolved star with a spectroscopically derived stellar radius and mass of ... and ... , respectively, and a very close-in transiting planet, with a/Rlow * = 3.4. Radial velocity (RV) follow-up using the HARPS, FIES, and PFS instruments leads to a planetary mass of ... In combination with a radius measurement of 8.3 + or - 1.1 R+ in circle, this results in a mean planetary density of ... g cm super(-3). We furthermore discover a long-term RV trend, which may be caused by a long-period planet or stellar companion. Because K2-39b has a short orbital period, its existence makes it seem unlikely that tidal destruction is wholly responsible for the differences in planet populations around subgiant and main-sequence stars. Future monitoring of the transits of this system may enable the detection of period decay and constrain the tidal dissipation rates of subgiant stars.