The rapid development of information technology turned internet as the basic means and wide choice for communications. Due to extensive adoption of internet for communications it is essential these days to conceal the message from unintended reader. The present paper describes a new encryption algorithm using Chebyshev polynomial of I kind. The plain text is encrypted in three rounds each round consisting of two stages with the concatenation of the previous cipher character with different keys. For making the algorithm more secure the key for the first round of encryption is generated from the main key (agreed upon by the sender and the receiver) and the subsequent round keys are concatenated with the previous round keys. The stream cipher proposed here has several advantages over conventional cryptosystems.