The purpose of this study is to find out what effects, good and/or bad, the combination of sorafenib and dacarbazine has on sarcoma. Recurrent sarcoma is difficult to treat. Standard chemotherapy drugs can be toxic, and the length of benefit is usually short. As a result, we need new treatments for sarcoma. Sorafenib is a new type of "targeted" chemotherapy that attacks specific proteins (including "raf" and "VEGF receptor") in cells. We hope that by blocking these proteins we can cause the tumor to shrink. Sorafenib is also known as BAY 43-9006 and by the trade name Nexavar®. The FDA approved sorafenib in December of 2005 to treat patients with kidney cancer and in November of 2007 to treat patients with liver cancer. This drug is not approved by the U.S. Food and Drug Administration (FDA) or any other licensing authority for the treatment of sarcoma and is therefore considered to be experimental in this setting.

Inclusion Criteria:

• Patients must have histologically or cytologically confirmed leiomyosarcoma, synovial sarcoma or malignant peripheral nerve sheath tumor (MPNST).
• Patients with metastatic, locally advanced, unresectable or locally recurrent disease.
• Zero to two prior chemotherapy regimens including neoadjuvant or adjuvant therapy.
• Measurable disease as defined by RECIST 1.1.
• Age ≥ 18.
• Karnofsky performance status of 50%-100%.
• Adequate bone marrow, liver and renal function as assessed by the following:

Hemoglobin ≥ 8.5 g/dl Absolute neutrophil count (ANC) ≥ 1,500/mm3 Platelet count ≥ 75,000/mm3 Total bilirubin < or = to 1.5 times ULN ALT and AST < or = to 2.5 times the ULN ( < or = to 5 x ULN for patients with liver involvement) Creatinine < or = to 1.5 times ULN

• Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment.
• Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Patients should use adequate birth control for at least three months after the last administration of sorafenib.
• Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures.
• INR < 1.5 or a PT/PTT within normal limits if not on anticoagulation. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable.

Exclusion Criteria:

• Prior therapy with dacarbazine, sorafenib or other antiangiogenic agents.
• Chemotherapy within 3 weeks or radiotherapy within 2 weeks of first day of protocol therapy.
• More than two prior chemotherapy regimens.
• Known brain metastasis. Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis.
• Pregnancy or nursing.
• Social situation or psychiatric illness that would limit compliance with study requirements.
• Cardiac disease: Congestive heart failure > class II NYHA. Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months.
• Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy.
• Uncontrolled hypertension defined as systolic blood pressure > 150 mmHg or diastolic pressure > 90 mmHg for more than 24 hours, despite optimal medical management.
• Known human immunodeficiency virus (HIV) infection or chronic Hepatitis B or C.
• Active clinically serious infection > CTCAE Grade 2.
• Thrombotic or embolic events such as a cerebrovascular accident, transient ischemic attack or myocardial infarction within the past 6 months, or deep venous thrombosis or pulmonary embolism within two months.
• Pulmonary hemorrhage/bleeding event > or = to CTCAE Grade 2 within 4 weeks of first dose of study drug.
• Any other hemorrhage/bleeding event > or = to CTCAE Grade 3 within 4 weeks of first dose of study drug.
• Serious non-healing wound, ulcer, or bone fracture.
• Evidence or history of bleeding diathesis or coagulopathy.
• Any history of grade 4 thrombocytopenia (Plt <25,000), Grade 3 thrombocytopenia (Plt <50,000, >25,000) lasting 7 days or longer, or history of platelet transfusions for chemotherapy induced thrombocytopenia
• Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug.
• Use of St. John's Wort or rifampin (rifampicin).
• Known or suspected allergy to sorafenib or any agent given in the course of this trial.
• Any condition that impairs patient's ability to swallow pills.
• Any malabsorption problem that in the opinion of the investigator would interfere with the patients ability to tolerate oral sorafenib.