Neonatal abstinence syndrome is a condition that affects newborns who are exposed to chronic opioid drugs while they are in a mother's uterus (womb) prior to birth. The current standard of care treatment includes morphine sulfate. Buprenorphine is a drug used in adults to treat narcotic dependence and withdrawal, but has not yet been approved for use in newborns as a treatment alternative for Neonatal Abstinence Syndrome. This investigation is designed to measure if sublingual (under the tongue) buprenorphine is able to reduce hospital length of stay and decrease number of days of drug treatment currently required in treatment of NAS. Another goal will be to understand buprenorphine as a cost effective treatment for NAS.