This work presents a search for neutrinoless double beta decay of 136Xe using data from the EXO-200 detector collected between 2011 and 2012. Neutrinoless double beta decay (ββ0ν) is a hypothetical nuclear decay possible only if the neutrino is massive and is a Majorana particle. Observation of this process would constitute a measurement of the absolute neutrino mass scale, which is known to be non-zero from neutrino oscillation experiments. EXO-200 is a liquid xenon time projection chamber located at the Waste Isolation Pilot Plant (WIPP) in Carlsbad, NM. The detector is filled with 200 kg of liquid xenon isotopically enriched to 80.6%, used as both detection medium and decay source. Spectral fits based on detailed Monte Carlo simulations are used to constrain the number of events in the data. The analysis finds no evidence for ββ0ν in 136Xe, placing a lower limit on the half-life of 1.6 ·1025 yr at 90% confidence level. This implies an upper limit on the effective Majorana neutrino mass between 0.14-0.38 eV, one of the most stringent limits ever set on ββ0ν.