  In this letter, an alternative string theory in twistor space is proposed for
describing perturbative N=4 super-Yang-Mills theory. Like the recent proposal
of Witten, this string theory uses twistor worldsheet variables and has
manifest spacetime superconformal invariance. However, in this proposal,
tree-level super-Yang-Mills amplitudes come from open string tree amplitudes as
opposed to coming from D-instanton contributions.
