Complex organic compounds, including many important to life on Earth, are commonly found in meteoritic and cometary samples, though their origins remain a mystery. We examined whether such molecules could be produced within the solar nebula by tracking the dynamical evolution of ice grains in the nebula and recording the environments to which they were exposed. We found that icy grains originating in the outer disk, where temperatures were less than 30 kelvin, experienced ultraviolet irradiation exposures and thermal warming similar to that which has been shown to produce complex organics in laboratory experiments. These results imply that organic compounds are natural by-products of protoplanetary disk evolution and should be important ingredients in the formation of all planetary systems, including our own.