The purpose of this trial is to study how long patients can remain progression free when they receive CP-675,206, compared to how long patients can remain progression free when they receive best supportive care. If you choose to take part, you will be randomized to receive either CP-675,206 as maintenance therapy or best supportive care. Best supportive care means you will not receive any study drug or other treatment for your cancer. Best supportive care could include treatment with antibiotics, analgesic drugs (medicine for pain), blood transfusions or psychosocial and nutritional support, depending on your needs. You have a 50% chance of being randomized to receive CP-675,206.

Inclusion Criteria:

• Stage IIIb (with effusion) or stage IV disease that has responded or remained stable after 6 cycles of a platinum containing 1st-line regimen
• Patients must be able to be randomized between 3 and no more than 6 weeks after the last dose of first-line therapy.

Exclusion Criteria:

• No other systemic therapy except 1st-line platinum based treatment
• Symptomatic or uncontrolled brain mets or uncontrolled pleural effusions.