We developed a periodic version of density matrix embedding theory, DMET, with which it is possible to perform electronic structure calculations on periodic systems and compute the band structure of solid-state materials. Electron correlation can be captured by means of a local impurity model using various wave function methods, such as full configuration interaction, coupled cluster, and multiconfigurational methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real space-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Our results show that DMET is in good agreement with other many-body techniques at a cheaper computational cost. We anticipate that periodic DMET can be a promising first principle method for strongly correlated materials.