Parallel-detection electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM) and a field emission source provides an unprecedented sensitivity for elemental microanalysis. By deflecting the energy loss spectrum across a parallel detector and computing the difference spectrum from sequentially collected energy-shifted spectra, the effects due to detector pattern noise are nearly eliminated so that signals less than 0.1% of the background can be readily detected. Measurements on a series of glass standard reference materials show that EELS provides both high spatial resolution and trace sensitivity at the 10 atomic ppm level for a wide range of elements including the alkaline earths, 3-d transition metals, and the lanthanides. For analytical volumes with dimensions of the order of 10 nm, this translates into near-single atom detectability.