Blind demodulation (breaking) of chaotic direct sequence spread spectrum (CD3S) signals is a challenging and leading issue under multipath fading channel in the field of chaotic communication. Until now, there are neither equalization methods to remove the impact of the channel, nor the immediate breaking methods. Based on the existing study, the breakability of CD3S signals is analyzed under multipath fading channel by using unscented Kalman filter (UKF) chaotic fitting in this paper. Beginning with the state space equation for the CD3S signals in UKF chaotic fitting, the channel influence on the tracking error is analyzed in the process of UKF chaotic fitting, then the range of the message state estimation is derived, and finally a sufficient condition theorem is proposed for the CD3S signals to be broken. Simulation results show that CD3S signals can be broken successfully under the proposed condition with excellent performance of bit error rate (BER), no matter whether the channel characteristic is either time-invariant or time-variant.