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We report the discovery of WASP-34b, a sub-Jupiter-mass exoplanet transitingits 10.4-magnitude solar-type host star (1SWASP J110135.89-235138.4; TYC6636-540-1) every 4.3177 days in a slightly eccentric orbit (e = 0.038 +/-0.012). We find a planetary mass of 0.59 +/- 0.01 M_Jup and radius of 1.22^{+0.11}_{-0.08} R_Jup. There is a linear trend in the radial velocities of55+/-4 m/s/y indicating the presence of a long-period third body in the systemwith a mass > 0.45 M_Jup at a distance of >1.2 AU from the host star. Thisthird-body is either a low-mass star, white dwarf, or another planet. Thetransit depth ((R_P/R_*)^2 = 0.0126) and high impact parameter (b = 0.90)suggest that this could be the first known transiting exoplanet expected toundergo grazing transits, but with a confidence of only ~80%.

WASP-34b: a near-grazing transiting sub-Jupiter-mass exoplanet in a hierarchical triple system