We report field emission microscopy images from single walled carbon nanotubes showing resolvable fine structure with five- and six-fold symmetry. We present evidence indicating that these images have atomic resolution and that they depict the electronic structure of individual nanotube caps under high-field conditions. Fine structure is observed only after removal of surface adsorbates. Prior to adsorbate removal, these images show symmetrical lobed patterns and several other behaviors characteristic of chemisorbed resonant tunneling states. (C) 1999 American Institute of Physics. [S0021-8979(99)05907-1].