We report the discovery of nine previously unknown gamma-ray pulsars in a blind search of data from the Fermi Large Area Telescope (LAT). The pulsars were found with a novel hierarchical search method originally developed for detecting continuous gravitational waves from rapidly rotating neutron stars. Designed to find isolated pulsars spinning at up to kHz frequencies, the new method is computationally efficient, and incorporates several advances, including a metric-based gridding of the search parameter space (frequency, frequency derivative and sky location) and the use of photon probability weights. The nine pulsars have spin frequencies between 3 and 12 Hz, and characteristic ages ranging from 17 kyr to 3 Myr. Two of them, PSRs Jl803-2149 and J2111+4606, are young and energetic Galactic-plane pulsars (spin-down power above 6 x 10(exp 35) ergs per second and ages below 100 kyr). The seven remaining pulsars, PSRs J0106+4855, J010622+3749, Jl620-4927, Jl746-3239, J2028+3332,J2030+4415, J2139+4716, are older and less energetic; two of them are located at higher Galactic latitudes (|b| greater than 10 degrees). PSR J0106+4855 has the largest characteristic age (3 Myr) and the smallest surface magnetic field (2x 10(exp 11)G) of all LAT blind-search pulsars. PSR J2139+4716 has the lowest spin-down power (3 x l0(exp 33) erg per second) among all non-recycled gamma-ray pulsars ever found. Despite extensive multi-frequency observations, only PSR J0106+4855 has detectable pulsations in the radio band. The other eight pulsars belong to the increasing population of radio-quiet gamma-ray pulsars.