This　paper　proposes　a　code　index　modulated　chaotic　ambient　backscatter　communication　(CIM-CAmBC)　over　Rayleigh　fading　channels.　In　this　system,　multiple　bits　of　the　backscatter　device　can　be　transmitted　in　a　radio　frequency　(RF)　source　symbol　by　using　CIM　technique.　Moreover,　we　design　a　differential　Walsh　code　matrix　for　CIM　at　the　backscatter　device　such　that　direct-link　interference　(DLI)　can　be　effectively　eliminated　at　the　reader　without　acquisition　of　channel　state　information　(CSI).　The　theoretical　error　performance　of　the　proposed　CIM-CAmBC　over　multipath　fading　channels　is　derived　and　then　verified　by　simulations.　The　results　demonstrate　that　the　proposed　system　can　outperform　the　conventional　DCSK-AmBC　and　CIM-DCSK-AmBC　by　more　than　3　dB　over　fading　channels.　IEEE