The hypothesis is that (1) the peptide T-1249 will be safe and well-tolerated when given at doses up to 25 mg/day; and (2) plasma levels of T-1249 above the IC90 for HIV-1 (0.1 mg/mL) can be achieved by daily, or twice-daily, SC dosing of T-1249 at doses ranging from 6.25 - 25 mg/day. This is a Phase I clinical study which means this is the first time T-1249 will be given to a human being. T-1249 has been shown to block HIV-1 replication in test tubes. It works by keeping the HIV-1 virus from binding to the surface of certain cells in the immune system. During the past several years, 13 antiretroviral medicines have been approved by the FDA for the treatment of HIV-1 infected individuals. The drugs approved so far belong to one of two groups: either reverse transcriptase inhibitors or protease inhibitors. Researchers know that people who take these drugs, either alone or in various combinations, often develop resistance to the drugs over time. Furthermore, some of the currently approved drugs have side effects that are potentially harmful. Therefore, there is a need for the development of new, safe drugs that are different from those already in use. T-1249 is a special type of protein (peptide) that is being developed as a new approach for the treatment of HIV infection. Approximately 60 patients will be taking part in this study at eight clinical research centers nationwide. Because T-1249 is a peptide, it must be given by a shot that puts the medication in under the skin. Participants will be asked to make up to nine-scheduled clinic visits. After screening, study patients will be giving themselves subcutaneous injections, using a syringe of the same type that diabetics use to inject insulin.