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In this paper we give a natural and intrinsic criterion of the Chow, and Hilbert, stability for complex irreducible smooth projective curves $C\\subset \\mathbb P ^n$.\n  Namely, if the restriction $T\\mathbb P_{|C} ^n$ of the tangent bundle of $\\mathbb P ^n$ to $C$ is stable then $C\\subset \\mathbb P ^n$ is Chow stable, and hence Hilbert stable. 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