  We investigate the dynamics of a boson gas with three-body interactions in
dimensions $d=1,2$. We prove that in the limit of infinite particle number, the
BBGKY hierarchy of $k$-particle marginals converges to a limiting
(Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness
of solutions. Factorized solutions of the GP hierarchy are shown to be
determined by solutions of a quintic nonlinear Schr\"odinger equation. Our
proof is based on, and extends, methods of Erd\"os-Schlein-Yau,
Klainerman-Machedon, and Kirkpatrick-Schlein-Staffilani.
