A new CEPA-PNO (coupled electron pair approach with pair natural orbitals) method for the calculation of correlation energies in infinite periodic systems is proposed and applied to one- and two-dimensional He. The method starts from a crystal orbital Hartree-Fock (COHF) wavefunction with the occupied Bloch orbitals transformed into Wannier orbitals. The coupled-cluster equations for the infinite system are simplified by CEPA-type approximations : A CEPA-0 (or Linear coupled-cluster) formula is applied for the small intercell contributions to the total correlation energy while CI-SD, ACPF or other CEPA variants are used for the large intracell contributions. The enormous number of single and double excitations into the virtual space is greatly reduced by the use of pair natural orbitals (PNOs), which leads to large savings in the necessary computer time and disk storage. First applications to the van der Waals interaction in the linear chain and the hexagonal plane of He atoms, performed with medium size and large atomic basis sets, show that an accuracy can be reached for the infinite-systems which is comparable to the accuracy of the corresponding calculations for small He clusters. Because of the extended use of the translational symmetry of the Wannier orbitals, the calculations for the linear infinite systems are even considerably faster than those for the oligomers He-5 and He-7.