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In this paper, we propose a new stream cipher Gemstone by discretizing coupled map lattices (CML), which is a nonlinear system of coupled chaotic maps. Gemstone uses a 128-bit key and a 64-bit initialization vector (IV). We show that there is no high probability difference propagations or high correlations over the IV setup scheme. Thus the IV setup of Gemstone is very secure. We also verify that the largest linear correlations between consecutive key streams are below the safe bounds. Gemstone is slightly slower than AES-CTR, but its initialization speeds are higher than some finalists of eSTREAM. [ABSTRACT FROM AUTHOR]