In this paper, we propose to apply a novel chaos-based ultra-wide band (UWB) radar for through-the-wall imaging. The proposed chaos modulation offers superior resolution compared to conventional UWB radars when applied for through-the-wall imaging. A noncoherent receiver is designed based on expectation maximization (EM) algorithm. The theoretical detection performance is derived for through-the-wall detection in the presence and absence of room reverberations as a function of dielectric properties of walls, targets, and their geometry illustrating the robustness of the proposed modulation against room reverberations. The resolution of the proposed modulation is analyzed theoretically and verified through simulations for different wall materials. Numerical electromagnetic simulations using finite difference time domain (FDTD) method are performed to confirm the obtained theoretical results. From the theoretical and simulation analysis, we find that the proposed chaos-based pulse amplitude modulated ultra-wide band (CPAM-UWB) radar has better detection performance, penetrating ability and imaging performance compared to other conventional through-the-wall imaging radars.