Molecules and particles make up ∼40%–70% of carbon in the interstellar medium, yet the exact chemical structure of these constituents remains unknown. We present carbon K-shell absorption spectroscopy of the Galactic interstellar medium obtained with the Low Energy Transmission Grating Spectrometer on board the Chandra Observatory that directly addresses this question. We probe several lines of sight, using bright active galactic nuclei as backlighters. We make our measurements differentially with respect to the bright source Mrk 421, in order to take the significant carbon K absorption in the instrument into account. In the spectrum of the blazar 1ES 1553+113 we find evidence for a novel feature: strong extinction on the low-energy side of the neutral C 1s−2p resonance, which is indicative of scattering by graphite particles. We find evidence for characteristic particle radii of order 0.1–0.15 μm. If this explanation for the feature is correct, limits on the mass of the available carbon along the line of sight may imply that the grains are partially aligned, and the X-rays from the source may have intrinsic polarization.