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 −2.2 × 10−11 Hz s−1, implying a young characteristic age of 4970 yr and a large spin-down power of 5.9 × 1036 erg s−1. Follow-up observations with radio telescopes detected no pulsations; thus PSR J1838−0537 appears radio-quiet as viewed from Earth. In 2009 September the pulsar suffered the largest glitch so far seen in any gamma-ray-only pulsar, causing a relative increase in spin frequency of about 5.5 × 10−6. 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 LAT’s sky-survey observing pattern. The pulsar’s 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.