We report ultrafast measurements of thermal transport in plasma polymerized CHF3 films deposited on standard Si substrates with Al sputtered on top. We characterize the thin films by X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), and spectroscopic ellipsometry and measure polymer thicknesses ranging from 33 nm down to 6 nm. Time-domain thermoreflectance (TDTR) provides quantitative data on the polymer thermal response to periodic heating from a pulsed laser source. A pump beam heats the Al layer, which acts as an opto-thermal transducer to the stack (Al-Polymer-Si) and a delayed probe beam measures the change in Al surface reflectance. We extract the polymer thermal conductivity by comparing TDTR data to a thermal diffusion model and find it to increase with decreasing polymer thicknesses below 30 nm.