This paper studies the security of a recently-proposed 3D chaotic self-synchronization stream cipher. Ac­cording to the chosen-ciphertext attack, a single key decipher algorithm is further investigated. First, multiple pairs of plaintext-ciphertext are obtained by choosing the corresponding multiple frames of ciphertext as fixed values. And then a set of possible estimated values for this single key is acquired by utilizing among one pair of plaintext-ciphertext. Fi­nally, the only estimated value that satisfies the all conditions of multiple pairs of plaintext-ciphertext is determined, as an estimated value from the set of possible estimated values. Security performance analysis results have shown that, under the condition that only one unknown key needs to be deciphered while the remaining keys are all known, the proposed algorithm can respectively decipher each individual key accurately. In addition, the attack complexity of the proposed method is lower than that of the exhaustive attack.