In this paper, we report the evidence for a planetary mass body orbiting the close binary star KIC 5095269. This detection arose from a search for eclipse timing variations among the more than 2,000 eclipsing binaries observed by Kepler. Light curve and periodic eclipse time variations have been analysed using Systemic and a custom Binary Eclipse Timings code based on the Transit Analysis Package which indicates a $7.70±0.08M_{Jup}$ object orbiting every $237.7±0.1d$ around a $1.2M_⊙$ primary and $0.51M_⊙$ secondary in an 18.6d orbit. A dynamical integration over $10^7$ years suggests a stable orbital configuration. Radial velocity observations are recommended to confirm the properties of the binary star components and the planetary mass of the companion. ; Comment: 8 pages, 7 figures, Accepted for publication in MNRAS