Evaluation of Safety, Tolerability, Pharmacokinetics, and Antiretroviral Activity of Ulonivirine (MK-8507) in Human Immunodeficiency Virus (HIV-1)-Infected Participants (MK-8507-003)

Inclusion Criteria: * Male, or non-pregnant and non-breastfeeding female, or postmenopausal or surgically sterile female (confirmed with medical records, examination, or laboratory test). Male participants with female partner of childbearing potential agrees to use a medically acceptable method of contraception during the study and 90 days after receiving study drug. * Body mass index \<=35 kg/m\^2 * Other than HIV infection, baseline health judged to be stable at screening and/or prior to administration of study drug * No clinically-significant electrocardiogram abnormality * Documented to be HIV-1 positive as determined by a positive enzyme-linked immunosorbent assay (ELISA) or quantitative polymerase chain reaction (PCR) result with confirmation * Has a screening plasma Cluster of Differentiation (CD4) T-cell count of \>200 /mm\^3 * Has a plasma HIV-1 RNA \>= 10,000 copies/mL within 30 days before administration of study drug * ART-naive, defined as never having received any ART agent, or have received \<=30 consecutive days of an investigational ART agent, excluding non-nucleoside reverse transcriptase inhibitors (NNRTIs), or have received \<=60 consecutive days of combination ART, excluding NNRTIs * Has not received an investigational agent or licensed ART within 30 days of study drug administration * Diagnosed with HIV-1 infection \>=3 months before screening * Willing to receive no other ART for the duration of the study * Has no evidence of mutations conferring resistance to NNRTIs at screening Exclusion Criteria: * Mentally or legally institutionalized or incapacitated, has significant emotional problems, or has a history of clinically significant psychiatric disorder * History of clinically significant and not stably controlled abnormalities or diseases * History of cancer, with the exceptions of 1) adequately-treated non-melanomatous skin carcinoma or carcinoma in situ of the cervix, 2) other malignancies which have been successfully treated \>=10 years before screening, or 3) participants who are highly unlikely to sustain a recurrence for the duration of the study * History of significant multiple and/or severe allergies, or has had an anaphylactic reaction or significant intolerability to drugs or food * Positive for hepatitis B surface antigen * History of chronic hepatitis C virus (HCV) unless there has been a documented cure or a negative HCV viral load * Had major surgery, or donated or lost \>=1 unit (\~500 mL) of blood within 4 weeks before screening * Participated in another investigational trial within 4 weeks before administration of study drug * Unable to refrain from or anticipates the use of any medication beginning 4 weeks before administration of study drug and throughout the trial. Certain medications are permitted. * Consumes \>3 glasses of alcoholic beverages per day (1 glass is equivalent to 12 ounces of beer, 4 ounces of wine, or 1 ounce of distilled spirits). Participants who consume 4 glasses of alcoholic beverages per day may be enrolled at the discretion of the investigator. * Consumes \>10 cigarettes per day and is unwilling to restrict smoking to \<=10 cigarettes per day * Regular user of any illicit drugs or has a history of drug abuse (including alcohol) within 2 years * Has an immediate family member who is investigational site or sponsor staff directly involved with the trial