Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state. emails: salexander@itp.stanford.edu, jjmaleck@uwaterloo.ca, lsmolin@perimeterinstitute.ca 1