Borderline personality disorder (BPD) is a chronic disorder in emotional regulation and is characterized by instability in self-image, mood, relationships, and behavior. People suffering from BPD have a high rate of self-injury and suicide attempts. This study will compare the effectiveness of two treatments for preventing self-injury and suicide in people with BPD: dialectical behavior therapy (DBT) and fluoxetine with clinical management. DBT is a behavioral therapy that teaches new coping skills to replace old strategies, including self-injury and attempted suicide. Fluoxetine is a selective serotonin reuptake inhibitor (SSRI) medication that has been used to treat BPD. Clinical management of fluoxetine, which is involved in administering the medication under normal conditions, refers to regular visits with a psychiatrist who will monitor medication effectiveness and side effects. Clinical management in this study may include adjusting the dosage of fluoxetine or prescribing a change in medication to citalopram, another SSRI.