We report the discovery of HAT-P-14b, a fairly massive transiting extrasolar planet orbiting the moderately bright star GSC 3086-00152 (V = 9.98), with a period of P = 4.627669 +/- 0.000005 days. The transit is close to grazing (impact parameter 0.891 +0.007/-0.008) and has a duration of 0.0912 +/- 0.0017 days, with a reference epoch of mid transit of Tc = 2454875.28938 +/- 0.00047 (BJD). The orbit is slightly eccentric (e = 0.107 +/- 0.013), and the orientation is such that occultations are unlikely to occur. The host star is a slightly evolved mid-F dwarf with a mass of 1.386 +/- 0.045 M(Sun), a radius of 1.468 +/- 0.054 R(Sun) effective temperature 6600 +/- 90 K, and a slightly metal-rich composition corresponding to [Fe/H] = +0.11 +/- 0.08. The planet has a mass of 2.232 +/- 0.059 M(Jup) and a radius of 1.150 +/- 0.052 R(Jup), implying a mean density of 1.82 +/- 0.24 g/cm3. Its radius is well reproduced by theoretical models for the 1.3 Gyr age of the system if the planet has a heavy-element fraction of about 50 M(Earth) (7% of its total mass). The brightness, near-grazing orientation, and other properties of HAT-P-14 make it a favorable transiting system to look for changes in the orbital elements or transit timing variations induced by a possible second planet, and also to place meaningful constraints on the presence of sub-Earth mass or Earth mass exomoons, by monitoring it for transit duration variations.
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