We use a high harmonic generated supercontinuum in the soft X-ray region to measure X-ray absorption near edge structure (XANES) spectra in polythiophene (poly(3-hexylthiophene)) films at multiple absorption edges. A few-cycle carrier-envelope phase-stable laser pulse centered at 1800 nm was used to generate a stable soft X-ray supercontinuum, with amplitude gating limiting the generated pulse duration to a single optical half-cycle. We report a quantitative transmission measurement of the sulfur L2,3 edge over the range 160-200 eV and the carbon K edge from 280 to 330 eV. These spectra show all the features previously reported in the XANES spectra of polythiophene, but for the first time they are measured with a source that has an approximately 1 fs pulse duration. This study opens the door to measurements that can fully time-resolve the photoexcited electronic dynamics in these systems.