  We report the experimental realization of an optical trap that localizes
single Cs atoms ~215 nm from surface of a dielectric nanofiber. By operating at
magic wavelengths for pairs of counter-propagating red- and blue-detuned
trapping beams, differential scalar light shifts are eliminated, and vector
shifts are suppressed by ~250. We thereby measure an absorption linewidth
\Gamma/2\pi = 5.7 \pm 0.1 MHz for the Cs 6S1/2,F=4 - 6P3/2,F'=5 transition,
where \Gamma/2\pi = 5.2 MHz in free space. Optical depth d~66 is observed,
corresponding to an optical depth per atom d_1~0.08. These advances provide an
important capability for the implementation of functional quantum optical
networks and precision atomic spectroscopy near dielectric surfaces.
