Summary: We study a new mechanism for the onset of chaos in coupled map lattices. The lattice dynamics becomes chaotic when the strength of spatial interactions exceeds some threshold. This transition is generated by the bifurcation that we call a peak-crossing one. It is shown that this mechanism can generate chaotic motion even in some coupled map lattices with extremely simple local dynamics. The resulting regime of chaos is characterized by space intermittency when the lattice is partitioned into alternating clusters that move chaotically and periodically, respectively.