The upper critical field, H(c2), of Mg(B1-xCx)(2) has been measured in order to probe the maximum magnetic field range for superconductivity that can be attained by C doping. Carbon doped MgB2 filaments were prepared, and for carbon levels below 4% the transition temperatures are depressed by about 1 K/% C and H(c2)(T=0) rises by about 5 T/% C. This means that 3.8% C substitution will depress T(c) from 39.2 to 36.2 K and raise H(c2)(T=0) from 16.0 to 32.5 T. These rises in H(c2) are accompanied by a rise in resistivity at 40 K from about 0.5 to about 10 microOmega cm.