The primary goal of this Phase I/II study is to assess the immune response and safety of recombinant human CD40 ligand (rhuCD40L) in patients with X-linked hyper IgM syndrome (XHIM). XHIM is a rare genetic disease caused by mutations in the gene encoding CD40 ligand. Individuals with this syndrome fail to make gamma immune globulin, frequently suffer from opportunistic infections, and are at an increased risk of developing cancer. Despite treatment with gamma globulin replacement therapy, the expected survival of patients with XHIM is less than 20 percent by the age of 25.