A background-free observation of cold antihydrogen atoms is made using field ionization followed by antiproton storage, a detection method that provides the first experimental information about antihydrogen atomic states. More antihydrogen atoms can be field ionized in an hour than all the antimatter atoms that have been previously reported, and the production rate per incident high energy antiproton is higher than ever observed. The high rate and the high Rydberg states suggest that the antihydrogen is formed via three-body recombination.