We report the discovery and timing measurements of PSR J1208 - 6238 , a young and highly magnetized gamma-ray pulsar , with a spin period of 440 ms . The pulsar was discovered in gamma-ray photon data from the Fermi Large Area Telescope ( LAT ) during a blind-search survey of unidentified LAT sources , running on the distributed volunteer computing system Einstein @ Home . No radio pulsations were detected in dedicated follow-up searches with the Parkes radio telescope , with a flux density upper limit at 1369 MHz of 30 \mu Jy . By timing this pulsar ’ s gamma-ray pulsations , we measure its braking index over five years of LAT observations to be n = 2.598 \pm 0.001 \pm 0.1 , where the first uncertainty is statistical and the second estimates the bias due to timing noise . Assuming its braking index has been similar since birth , the pulsar has an estimated age of around 2,700 yr , making it the youngest pulsar to be found in a blind search of gamma-ray data and the youngest known radio-quiet gamma-ray pulsar . Despite its young age the pulsar is not associated with any known supernova remnant or pulsar wind nebula . The pulsar ’ s inferred dipolar surface magnetic field strength is 3.8 \times 10 ^ { 13 } G , almost 90 \% of the quantum-critical level . We investigate some potential physical causes of the braking index deviating from the simple dipole model but find that LAT data covering a longer time interval will be necessary to distinguish between these .