Directly detecting thermal emission from young extrasolar planets allows measurement of their atmospheric composition and luminosity, which is influenced by their formation mechanism. Using the Gemini Planet Imager, we discovered a planet orbiting the \$sim$20 Myr-old star 51 Eridani at a projected separation of 13 astronomical units. Near-infrared observations show a spectrum with strong methane and water vapor absorption. Modeling of the spectra and photometry yields a luminosity of L/LS=1.6-4.0 x 10-6 and an effective temperature of 600-750 K. For this age and luminosity, "hot-start" formation models indicate a mass twice that of Jupiter. This planet also has a sufficiently low luminosity to be consistent with the "cold- start" core accretion process that may have formed Jupiter.