The Investigators hope to learn if they can prevent or lessen the symptoms of neonatal abstinence syndrome (NAS) in babies born to narcotic-dependent mothers by using the drug ondansetron in the mothers and their babies. The study is a randomized, double-blind, placebo-controlled study with one half the mother-baby pairs to receive ondansetron and the other half of the mother-baby pairs to receive placebo. The Investigators plan to give the pregnant narcotic-dependent mothers an intravenous dose of study medication prior to delivery and after the baby is born, the neonate will receive the same study medication the mother received every 24 hours for up to 5 days. The Investigators will follow up with the mother-baby pairs for 10 days after study drug has stopped and one last follow up, about 30 days after stopping study drug, to see if the baby had any symptoms of NAS.