We report the discovery of PSR J1838-0537, a gamma-ray pulsar found through a blind search of data from the Fermi Large Area Telescope (LAT). The pulsar has a spin frequency of 6.9 Hz and a frequency derivative of -2.2e-11 Hz/s, implying a young characteristic age of 4970 years and a large spin-down power of 5.9e36 erg/s. Follow-up observations with radio telescopes detected no pulsations, thus PSR J1838-0537 appears radio-quiet as viewed from Earth. In September 2009 the pulsar suffered the largest glitch so far seen in any gamma-ray-only pulsar, causing a relative increase in spin frequency of about 5.5e-6. After the glitch, during a putative recovery period, the timing analysis is complicated by the sparsity of the LAT photon data, the weakness of the pulsations, and the reduction in average exposure from a coincidental, contemporaneous change in the LATs sky-survey observing pattern. The pulsars sky position is coincident with the spatially extended TeV source HESS J1841-055 detected by the High Energy Stereoscopic System (H.E.S.S.). The inferred energetics suggest that HESS J1841-055 contains a pulsar wind nebula powered by the pulsar.