  We suggest using an evanescent wave around a thin fiber to trap atoms. We
show that the gradient force of a red-detuned evanescent-wave field in the
fundamental mode of a silica fiber can balance the centrifugal force when the
fiber diameter is about two times smaller than the wavelength of the light and
the component of the angular momentum of the atoms along the fiber axis is in
an appropriate range. As an example, the system should be realizable for Cesium
atoms at a temperature of less than 0.29 mK using a silica fiber with a radius
of 0.2 $\mu$m and a 1.3-$\mu$m-wavelength light with a power of about 27 mW.
