We report the discovery of HAT-P-24b , a transiting extrasolar planet orbiting the moderately bright V=11.818 F8 dwarf star GSC 0774-01441 , with a period P = 3.3552464 \pm 0.0000071 d , transit epoch T _ { c } = 2455216.97669 \pm 0.00024 ( BJD Barycentric Julian dates throughout the paper are calculated from Coordinated Universal Time ( UTC ) ) , and transit duration 3.653 \pm 0.025 hours . The host star has a mass of 1.191 \pm 0.042 M _ { \sun } , radius of 1.317 \pm 0.068 R _ { \sun } , effective temperature 6373 \pm 80 K , and a low metallicity of [ Fe / H ] = -0.16 \pm 0.08 . The planetary companion has a mass of 0.681 \pm 0.031 M _ { J } , and radius of 1.243 \pm 0.072 R _ { J } yielding a mean density of 0.439 \pm 0.069 g cm ^ { -3 } . By repeating our global fits with different parameter sets , we have performed a critical investigation of the fitting techniques used for previous HAT planetary discoveries . We find that the system properties are robust against the choice of priors . The effects of fixed versus fitted limb darkening are also examined . HAT-P-24b probably maintains a small eccentricity of e = 0.052 _ { -0.017 } ^ { +0.022 } , which is accepted over the circular orbit model with false alarm probability 5.8 % . In the absence of eccentricity pumping , this result suggests HAT-P-24b experiences less tidal dissipation than Jupiter . Due to relatively rapid stellar rotation , we estimate that HAT-P-24b should exhibit one of the largest known Rossiter-McLaughlin effect amplitudes for an exoplanet ( \Delta V _ { RM } \simeq 95 m/s ) and thus a precise measurement of the sky-projected spin-orbit alignment should be possible .