Natalizumab is a humanized monoclonal antibody currently being investigated as a potential treatment for Crohn's disease. It is believed to work by preventing white blood cells from moving from the blood stream into the bowel tissue. These cells are thought to cause damage to the bowel, leading to the symptoms of Crohn's disease. Elan Pharmaceuticals is currently sponsoring an international study evaluating the safety and efficacy of natalizumab in individuals with moderately to severely active Crohn's disease. Individuals with Crohn's disease will be randomly assigned to receive either placebo (an inactive solution) or natalizumab by intravenous infusion (this means putting it directly into a vein in the arm). There will be a one out of two chance of receiving natalizumab and a one out of two chance of receiving placebo. Participants in the study will receive several infusions of natalizumab or placebo at 4-week intervals. Eligible participants will then have the opportunity to enroll into an extension study that will allow all participants to receive natalizumab. For those patients who do not enroll into the extension study, the total participation in this study will last for approximately 22 weeks.