We report the discovery from K2 of a transiting planet in an 18.25-d, eccentric (0.19$pm$ 0.04) orbit around K2-99, an 11th magnitude subgiant in Virgo. We confirm the planetary nature of the companion with radial velocities, and determine that the star is a metal-rich ([Fe/H] = 0.20$pm$0.05) subgiant, with mass $1.60^{+0.14}_{-0.10}~M_odot$ and radius $3.1pm 0.1~R_odot$. The planet has a mass of $0.97pm0.09~M_{rm Jup}$ and a radius $1.29pm0.05~R_{rm Jup}$. A measured systemic radial acceleration of $-2.12pm0.04~{rm m s^{-1} d^{-1}}$ offers compelling evidence for the existence of a third body in the system, perhaps a brown dwarf orbiting with a period of several hundred days.
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