[Show abstract][Hide abstract] ABSTRACT: Context. The Large Magellanic Cloud (LMC) is to date the only normal external galaxy that has been detected in high-energy gamma rays. High-energy gamma rays trace particle acceleration processes and gamma-ray observations allow the nature and sites of acceleration to be studied. Aims. We characterise the distribution and sources of cosmic rays in the LMC from analysis of gamma-ray observations. Methods. We analyse 11 months of continuous sky-survey observations obtained with the Large Area Telescope aboard the Fermi Gamma-Ray Space Telescope and compare it to tracers of the interstellar medium and models of the gamma-ray sources in the LMC. Results. The LMC is detected at 33σ significance. The integrated >100 MeV photon flux of the LMC amounts to (2.6 ± 0.2) × 10-7 ph cm-2 s-1 which corresponds to an energy flux of (1.6 ± 0.1) × 10-10 erg cm-2 s-1, with additional systematic uncertainties of 16%. The analysis reveals the massive star forming region 30 Doradus as a bright source of gamma-ray emission in the LMC in addition to fainter emission regions found in the northern part of the galaxy. The gamma-ray emission from the LMC shows very little correlation with gas density and is rather correlated to tracers of massive star forming regions. The close confinement of gamma-ray emission to star forming regions suggests a relatively short GeV cosmic-ray proton diffusion length. Conclusions. The close correlation between cosmic-ray density and massive star tracers supports the idea that cosmic rays are accelerated in massive star forming regions as a result of the large amounts of kinetic energy that are input by the stellar winds and supernova explosions of massive stars into the interstellar medium.