We use a laboratory version of the intergenerational goods game (IGG) to investigate whether peer punishment facilitates the successful provision of multigenerational public goods. In our experiment, groups (generations) decide sequentially about the provision of a multigenerational public good through the voluntary contributions of their members. Successful provision requires that contributions meet a threshold and exclusively benefits members of future generations. Provision costs are borne only by the current generation. We compare a baseline condition without a punishment institution to a treatment condition where peer punishment can be inflicted exclusively on members of the same generation but not on members of past or future generations. We find that without punishment the likelihood of reaching the contribution threshold is low and that making punishment available within a generation is partially successful in sustaining cooperation in a succession of multiple generations.