We present an analysis of the abundance of interstellar carbon toward six stars within 600 pc of the Sun based upon high signal-to-noise (S/N similar or equal to 400-600) data of the weak intersystem line C II] lambda 2325 Angstrom obtained with the Goddard High Resolution Spectrograph aboard the Hubble Space Telescope. We find that the measured gas-phase C/H shows no dependence on either direction or the physical condition of the gas and that 10(6) C/H similar or equal to 140 +/- 20. Our sample of sight lines includes examples exhibiting a wide range of extinction variation, including features traditionally associated with carbon grains (e.g., the 2175 Angstrom bump). The lack of any statistically significant variation in the observed gas-phase C/H among these sight lines strongly suggests that the source of this variation in extinction is probably not variations in the dust abundance of carbon. Based upon an assessment of the total interstellar abundance of oxygen (i.e., gas and dust) along with comparisons to O/H and C/H observed in B stars, we adopt an intrinsic (i.e., cosmic) abundance for carbon in the local ISM of 10(6)(C/H)(cosmic) similar or equal to 240 +/- 50. From the observed gas-phase C/H, we argue that the dust-phase carbon abundance must then be 50 < 10(6)(C/H)(dust) < 150. This amount of solid carbon can explain such extinction features as the 2175 Angstrom bump (i.e., graphite and/or PAHs) but puts severe restrictions on the availability of carbon in grains to explain the total optical/UV dust opacity.