A set is primitive if no element of the set divides another. We consider primitive sets of monic polynomials over a finite field and find natural generalizations of many of the results known for primitive sets of integers. In particular we generalize a result of Besicovitch to show that there exist primitive sets in Fq[x] with upper density arbitrarily close to q−1 q . Then, for a primitive set A, we consider the sum a∈A 1 q deg a deg a , the natural analogue in this setting of a sum considered by Erdős for primitive subsets of the integers, and show that it is uniformly bounded over all primitive sets A. We end with a generalization of work of Martin and Pomerance on the asymptotic growth rate of the counting function of a primitive set. Along the way we prove a quantitative analogue of the Hardy-Ramanujan theorem for function fields, as well as bounds on the size of the k-th irreducible polynomial.

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