The purpose of this study is to determine the safety and efficacy of administration of a cell-delivered ribozyme gene transfer product to participants with chronic (lasting a long time) Human Immunodeficiency Virus Type 1 (HIV-1) infection (a life-threatening infection which you can get from an infected person's blood or from having sex with an infected person).

This is a randomized (study drug assigned by chance), double-blind (neither the participant nor the physician know the study medication drug name), placebo (an inactive substance that is compared with a drug to test if the drug has a real effect in a clinical trial) controlled study to investigate safety and efficacy of administration of autologous cluster of differentiation 34 (CD34+) cells transduced with placebo or an anti-HIV-ribozyme (OZ1) in participants with HIV-1 infection. The total study duration will be 100 weeks and will include following visits: screening, pre-infusion Days 1-7, Day 8, Week 1, 4, 8, 12, 16, 20, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 and 100. Before the administration of CD34+ final cell product, a number of procedures will be performed, including the injection of granulocyte colony-stimulating factor (G-CSF) to mobilize the CD34+ cells, apheresis and the transduction of the CD34+ cells with either OZ1 or placebo. Participants will be divided into two groups: one group will receive OZ1-containing CD34+ cells, the other group will receive CD34+ cells alone and will receive a single intravenous infusion (a fluid or a medicine delivered into a vein by way of a needle) of CD34+ cells transduced with either placebo or OZ1 gene transfer product. The final cell product contains approximately 2-20 x 10^7 cells/kilogram autologous CD34+ cell suspension transduced with either placebo or OZ1 gene transfer product. Primary efficacy will be assessed primarily by the amount of HIV ribonucleic acid (RNA) (viral load). Participants' safety will be monitored throughout the study.

Inclusion Criteria:

• An Human Immunodeficiency Virus 1 (HIV-1) infection for at least 6 months documented by positive HIV serology including confirmation by Western Blot
• Receiving either the first or second regimen of antiretroviral therapy (ART) defined as 3 or more antiretroviral drugs in combination
• A Viral load less than 400 copies per milliliter (copies/ml), as measured by Roche Amplicor HIV-1 Monitor assay, on 2 consecutive occasions, at least 7 days apart and within 45 days prior to granulocyte colony-stimulating factor (G-CSF) administration and the second measurement has to be within 14 days prior to G-CSF
• Cluster of Differentiation 4 (CD4+) cell count must be greater that 300 cells per cubic millimeter (cells/mm^3)
• Women and men (or their partners) had to agree to use a medically accepted form of contraception and safe sexual practices

Exclusion Criteria:

• Any previous or current Acquired Immunodeficiency Syndrome (AIDS) defining illness by the Center for Disease Control (CDC) case definition, including AIDS-related dementia (mental decline), with the exception of Kaposi's sarcoma (purple or brown cancerous pimples on the skin, often associated with AIDS)
• Clinically significant clinical laboratory results
• Participants with veins unsuitable for study related procedures
• Current ART that included antiretroviral agents which exhibited antagonism when used together (example, zidovudine and stavudine ), or current or previous ART that included hydroxyurea
• Current pregnancy or breastfeeding