Inclusion Criteria:

• Able to provide signed and dated informed consent prior to study-specific screening procedures.
• Histologically or cytologically confirmed leiomyosarcoma that is persistent, recurrent or metastatic.
• Measurable disease as defined by RECIST.
• Karnofsky performance status >= 70%
• Male or female patients of child-producing potential must agree to use contraception or avoidance of pregnancy measures during the study and for 30 days after the last infusion of ARQ 501.
• Hemoglobin (Hgb) >= 10 g/dL.
• Absolute neutrophil count (ANC) >= 1.5 x 10^9/L (>= 1,500/mm3).
• Platelet count >= 100 x 10^9/L (>= 100,000/mm3).
• Total bilirubin less than or equal to 1.5 x upper limit of normal (ULN) or less than or equal to 3.0 x ULN with metastatic liver disease.
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 2.5 x ULN less than or equal to 5.0 ULN with metastatic liver disease.
• Creatinine less than or equal to 1.5 x ULN.

Exclusion Criteria:

• Received three or more prior anticancer chemotherapy regimens.
• Have active, uncontrolled systemic infection considered opportunistic, life threatening or clinically significant at the time of treatment.
• Have received anticancer chemotherapy, immunotherapy, radiotherapy, surgery or investigational agents within four weeks of first infusion.
• Have symptomatic or untreated central nervous system (CNS) involvement.
• Are pregnant or breastfeeding.
• Previous exposure to ARQ 501.