This is a first-in-human (FIH) study of 42037788 (referred to as CNTO 0007), a cell therapy being tested to see if it may be useful in treating patients with ischemic cerebral infarction also known as stroke. Patients will be randomized (assigned by chance) to receive a single dose of CNTO 0007 or placebo (identical in appearance to CNTO 0007 but does not contain cells) by intravenous (IV) infusion (injection directly into a vein). Patients and study staff will not know if patients are assigned CNTO 0007 or the placebo. The study will be conducted in 2 stages (Stage A and Stage B). In Stage A, the highest dose of CNTO 0007 that does not cause unacceptable side effects, referred to as the maximum tolerated dose (MTD) will be determined to and administered to patients in Stage B of the study. In Stage A, 5 (up to 7) cohorts (groups) of 4-8 patients each will be administered a single IV infusion of CNTO 0007 or placebo 1-5 days (depending on cohort) after stroke (the first cohort of patients will receive the lowest dose of CNTO 0007 or placebo and each subsequent cohort will be administered a higher dose of CNTO 0007 or placebo until the MTD is determined). In Stage B, patients will be administered a single IV infusion of the MTD within a specified number of days after stroke.