A concept for a femtosecond pulse compressor based on underdense plasma prisms is presented. An analytical model is developed to calculate the spectral phase incurred and the expected pulse compression. A 2D particle-in-cell simulation verifies the analytical model. Simulated intensities ($\sim10^{16}$ W/cm$^2$) were orders of magnitude higher than the damage threshold for conventional gratings used in chirped pulse amplification. Theoretical geometries for compact (10s cm scale) compressors for 1 PW, 10 PW, and 100 PW power levels are proposed.