  We compute the structure of a quantized vortex line in a harmonically trapped
dilute atomic Bose-Einstein condensate using the Popov version of the
Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be
(meta)stable in a nonrotating trap even in the zero-temperature limit, thus
confirming that weak particle interactions induce the condensed gas a
fundamental property characterizing ``classical'' superfluids. We present the
structure of the vortex at ultralow temperatures and discuss the crucial effect
of the thermal gas component to its energetic stability.
