We numerically investigated the chaos time delay signature (TDS) suppression and bandwidth enhancement by electrical heterodyning. Chaos signals generated with a semiconductor laser subject to optical feedback typically have distinct loop frequency peaks in their power spectra corresponding to the reciprocals of the time delays, which deteriorates the performance in applications including chaos radar/lidar and fast random bit generation. By electrically heterodyning the chaos signal with a single frequency local oscillator, we show that the power in the chaos spectrum can be redistributed and a smoother spectrum with a broader effective bandwidth can be obtained. Compared with the chaos directly generated from a semiconductor laser subject to optical feedback, the amplitudes of the TDS (ρ(TDS)) measured under different feedback strengths can be suppressed up to 63% and the effective bandwidths can be enhanced up to 46% in average after the electrical heterodyning is applied.