Robust data hiding methods are basically used when rightful ownership is intended and/or transmitting channel is prone to noise. In this paper, a robust and secure data hiding method is proposed in Tchebichef domain. For feature extraction, remainders of Tchebichef coefficients are calculated according to Chinese remainder theorem (CRT). Distances of these remainders are utilized as the extracted features. These distances are then modified according to the hidden bits, to complete the embedding process. To reduce the chance of illegal access and increase the security of the proposed method, a closed-loop chaotic encryption system (CLCES) has been introduced. The proposed CLCES requires very little side information and produces extremely sensitive noise-like sequences with high security. Robustness and security of the proposed method have been analyzed. Comparison results with other related methods in the current literature confirm the superiority of the proposed method. Due to its simplicity, the proposed method is a good candidate for real-time data hiding applications.