We report on the discovery of HAT-P-11b, the smallest radius transiting extrasolar planet (TEP) discovered from the ground, and the first hot Neptune discovered to date by transit searches. HAT-P-11b orbits the bright (V=9.587) and metal rich ([Fe/H]=+0.31+/-0.05) K4 dwarf star GSC 03561-02092 with P=4.8878162+/-0.0000071 days and produces a transit signal with depth of 4.2mmag, the shallowest found by transit searches that is due to a confirmed planet. We present a global analysis of the available photometric and radial velocity (RV) data that result in stellar and planetary parameters, with simultaneous treatment of systematic variations. HAT-P-11b orbits in an eccentric orbit with e=0.198+/-0.046 and {omega}=355.2{deg}+/-17.3{deg}, causing a reflex motion of its parent star with amplitude 11.6+/-1.2m/s, a challenging detection due to the high level of chromospheric activity of the parent star. Our ephemeris for the transit events is T_c_=2454605.89132+/-0.00032 (BJD), with duration 0.0957+/-0.0012 days, and secondary eclipse epoch of 2454608.96+/-0.15 days (BJD).