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Strongly quasipositive links are those links which can be seen as closures ofpositive braids in terms of band generators. In this paper we give a necessarycondition for a link with braid index 3 to be strongly quasipositive, byproving that in that case it has positive Conway polynomial (that is, all itscoefficients are non-negative). We also show that this result cannot beextended to a higher number of strands, as we provide a strongly quasipositivebraid whose closure has non-positive Conway polynomial.

Strongly quasipositive links with braid index 3 have positive Conway polynomial