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Let C be an ACM (projectively normal) nondegenerate smooth curve inprojective 3-space, and suppose C is general in its Hilbert scheme - this isirreducible once the postulation is fixed. Answering a question posed byPeskine, we show the gonality of C is d-l, where d is the degree of the curve,and l is the maximum order of a multisecant line of C. Furthermore l=4 exceptfor two series of cases, in which the postulation of C forces every surface ofminimum degree containing C to contain a line as well. We compute the value ofl in terms of the postulation of C in these exceptional cases. We also show theClifford index of C is equal to the gonality minus 2.

Gonality of a general ACM curve in projective 3-space