We show that the van der Waals heterostructure formed by MoSe2 and WS2 provides a unique system with near degenerate interlayer and intralayer excitonic states. Photoluminescence measurements indicate that the charge transfer exciton states are approximately 50 meV below the MoSe2 exciton states, with a significant spectral overlap. The transient absorption of a femtosecond pulse was used to study the dynamics of the charge transfer excitons at room temperature. We found a lifetime of approximately 80 ps for the charge transfer excitons. A diffusion coefficient of about 14 cm(2) s(-1) was deduced, which is comparable to individual excitons in transition metal dichalcogenides.