  $MgB_2$ becomes superconducting just below 40 K. Whereas porous
polycrystalline samples of $MgB_2$ can be synthesized from boron powders, in
this letter we demonstrate that dense wires of $MgB_2$ can be prepared by
exposing boron filaments to $Mg$ vapor. The resulting wires have a diameter of
160 ${\mu}m$, are better than 80% dense and manifest the full $\chi =
-1/4{\pi}$ shielding in the superconducting state. Temperature-dependent
resistivity measurements indicate that $MgB_2$ is a highly conducting metal in
the normal state with $\rho (40 K)$ = 0.38 $\mu Ohm$-$cm$. Using this value, an
electronic mean free path, $l \approx 600~\AA$ can be estimated, indicating
that $MgB_2$ wires are well within the clean limit. $T_c$, $H_{c2}(T)$, and
$J_c$ data indicate that $MgB_2$ manifests comparable or better superconducting
properties in dense wire form than it manifests as a sintered pellet.
