Migraine headaches can be disabling and can interfere with work and a person's quality of life. Preventing these headaches before they start is the best option. Topiramate, an anti-seizure medication, has been shown to help prevent migraine headaches from occurring. This is an open-label study that is an extension of a previous study (CAPSS-276) of Topiramate in chronic migraine. It includes patients who completed the previous study or who stopped the study early after taking study drug for at least 4 weeks of maintenance treatment due to lack of efficacy. The current study will involve a 4-week Blinded Transition Phase during which patients will be titrated up to a daily topiramate dose of 100 milligrams (or the maximum tolerated dose, whichever is less). Then there will be a 12-week Open-Label Maintenance Phase during which the topiramate dose may be adjusted according to effectiveness and tolerance, but not to exceed a daily dose of 400 milligrams. After this period, patients will be tapered off topiramate (Taper/Exit Phase). The length of the taper/exit phase may vary based on the dose the patient was taking during the open label maintenance phase. While on topiramate, patients will record daily entries in their headache records. Patients will also be asked questions to help assess their quality of life. Both patients and doctors will be asked questions at the end of the study about their impressions of change with respect to the patient's migraine headaches. Patients will also have physical and neurological examinations and laboratory tests performed during the study. The objective of this study is to evaluate the long-term safety and effectiveness of topiramate for the prevention of chronic migraine headaches. Topiramate oral tablets, 25 milligrams per tablet, will be given in the morning and evening to a dose not to exceed 400 milligrams per day or to the maximum tolerated dose, whichever is less