MANYof the globular clusters in our Galaxy have probably undergone core collapse, and are currently re-expanding1,2. This re-expansion requires a central energy source. Previously proposed mechanisms are either inefficient or may produce unacceptably bright cores3. Here we explore the most conservative solution to this problem. We suggest that primordial binaries, for which there is now direct evidence4-6, could provide the necessary energy. We show that this mechanism leads to relatively large core sizes, containing ~1% of the total cluster mass. Such a cluster would have a resolvable core (with a size of the order of arcseconds) which would consist mostly of binaries.