  The upper critical field, $H_{c2}$, of Mg(B$_{1-x}$C$_x$)$_2$ has been
measured in order to probe the maximum magnetic field range for
superconductivity that can be attained by C doping. Carbon doped boron
filaments are prepared by CVD techniques, and then these fibers are then
exposed to Mg vapor to form the superconducting compound. The transition
temperatures are depressed about $1 K/%$ C and $H_{c2}(T=0)$ rises at about $5
T/%$ C. This means that 3.5% C will depress $T_c$ from $39.2 K$ to $36.2 K$ and
raise $H_{c2}(T=0)$ from $16.0 T$ to $32.5 T$. Higher fields are probably
attainable in the region of 5% C to 7% C. These rises in $H_{c2}$ are
accompanied by a rise in resistivity at $40 K$ from about $0.5 \mu \Omega cm$
to about $10 \mu \Omega cm$. Given that the samples are polycrystalline wire
segments, the experimentally determined $H_{c2}(T)$ curves represent the upper
$H_{c2}(T)$ manifold associated with $H\perp c$.
