We have observed parametric generation and amplification of ultracold atom pairs. A Rb-87 Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k(0) and spontaneously scattered into two final states with quasimomenta k(1) and k(2). Furthermore, when a seed of atoms was first created with quasimomentum k(1) we observed parametric amplification of scattered atoms pairs in states k(1) and k(2) when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.