We construct a class of cubic gauge-invariant actions for superstring field theory, gauge fix one of them and show that it reproduces the known superstring S-matrix. In our construction boson string fields are taken in the 0 picture and fermion string fields in the −12 picture. For 0 picture the bosonic kinetic term requires an insertion carrying −2 units of picture number. We construct all possible picture-changing operators with the required properties. We use the simplest of these to construct the superstring action we choose to analyze here. In the gauge b1 + b−1 = 0, the conformal mappings needed to evaluate the tree diagrams are algebraic, and this enables a completely explicit derivation of the Koba-Nielsen amplitudes. In this gauge the action formally linearizes, a phenomenon familiar from other Chern-Simons type theories. Nontrivial scattering amplitudes are obtained by approaching this gauge as a limit.