A data structure is presented that explicitly maintains the graph of a Voronoi diagram of N point sites in the plane or the dual graph of a convex hull of points in three dimensions while allowing insertions of new sites/points. Our structure supports insertions in Õ(N^3/4) expected amortized time, where Õ suppresses polylogarithmic terms. This is the first result to achieve sublinear time insertions; previously it was shown by Allen et al. that Θ(√N) amortized combinatorial changes per insertion could occur in the Voronoi diagram but a sublinear-time algorithm was only presented for the special case of points in convex position.