Single-Dose Study of MK-4250 Monotherapy in Anti-Retroviral Therapy-Naive, Human Immunodeficiency Virus (HIV)-1 Infected Participants (MK-4250-002)

The study will evaluate the safety, tolerability, pharmacokinetics, and anti-retroviral activity of MK-4250 monotherapy in anti-retroviral therapy (ART)-naïve, HIV-1 infected participants. The primary hypothesis of the study is that at a dose that is sufficiently safe and generally well tolerated, MK-4250 has superior antiretroviral activity compared to a historical placebo, as measured by change from baseline in plasma HIV-1 ribonucleic acid (RNA) (log10 copies/mL) at 168 hours postdose.

The study consists of 5 panels; Panel C (MK-4250 ≤600 mg) was removed from the study with Protocol Amendment 1.

Eligibility Criteria:
Inclusion Criteria:

* Male or non-pregnant and non-breast feeding female
* If female with reproductive potential: must demonstrate a serum β-human chorionic gonadotropin (β -hCG) level consistent with the nongravid state and agree to use a highly effective method of birth control until 30 days after the dose of trial drug
* If postmenopausal female: without menses for at least 1 year and has a documented follicle stimulating hormone (FSH) level in the postmenopausal range at pretrial (screening), AND/OR status post hysterectomy or oophorectomy
* Documented HIV-1 positive as determined by a positive Enzyme-linked Immunosorbent Assay (ELISA) or Quantitative Polymerase Chain Reaction (QT-PCR) with confirmation (e.g., Western Blot).
* No evidence at screening for mutations (e.g., E92Q, N55H, Q148K, Q148R and Y143R) affecting susceptibility to Integrase Strand Transfer Inhibitors (InSTIs)
* Diagnosed with HIV-1 infection ≥ 3 months prior to screening or confirmed chronic HIV infection
* Screening plasma Cluster of Differentiation (CD) 4+ T cell count of \>200/mm\^3
* Screening plasma HIV-1 RNA ≥5,000 copies/mL within 30 days prior to the treatment phase of this study
* Anti-retroviral therapy (ART)-naïve, which is defined as having never received any antiretroviral agent OR ≤30 consecutive days of an investigational antiretroviral agent which is not an InSTI and no exposure to such an investigational antiretroviral agent within 60 days prior to screening OR ≤60 consecutive days of combination ART which does not include an InSTI and no exposure to such ART within 60 days prior to screening
* Never received any InSTI
* Willing to receive no other ART for the duration of the treatment phase of this study
* Body Mass Index (BMI) ≤35 kg/m\^2
* Other than HIV infection, have baseline health judged to be stable

Exclusion Criteria:

* Mentally or legally institutionalized / incapacitated, or significant emotional problems at the time of pretrial (screening) visit or expected during the conduct of the trial or has a history of clinically significant psychiatric disorder within the last 5 years
* History of clinically significant endocrine, gastrointestinal, cardiovascular, hematological, hepatic, immunological (outside of HIV-1 infection), renal, respiratory, genitourinary or major neurological abnormalities or diseases
* History of cancer (malignancy). Exceptions: (1) adequately treated non-melanomatous skin carcinoma or carcinoma in situ of the cervix; (2) other malignancies which have been successfully treated ≥10 years prior to the pretrial (screening) visit with no evidence of recurrence; or, (3) deemed highly unlikely to sustain a recurrence for the duration of the trial
* History of significant multiple and/or severe allergies (e.g., food, drug, latex allergy); anaphylactic reaction or significant intolerability (i.e., systemic allergic reaction) to prescription or non-prescription drugs or food; or hereditary galactose intolerance, lactose deficiency, or glucose-galactose malabsorption.
* Positive for hepatitis B surface antigen
* History of chronic hepatitis C (HCV) infection. Participants with a documented cure and/or a positive serologic test for HCV with a negative HCV viral load may be included
* Major surgery or donated or lost 1 unit of blood (approximately 500 mL) within 4 weeks prior to the pretrial (screening) visit
* Participated in another investigational trial within 4 weeks prior to the Day 1 dosing visit. The 4 week window will be derived from the date of the last trial medication and / or blood collection in a previous trial and/or an adverse event related to trial drug to the Day 1 dosing visit of the current trial
* Unable to refrain from or anticipates the use of any medication, including prescription and non-prescription drugs or herbal remedies beginning approximately 2 weeks prior to administration of the initial dose of trial drug, throughout the trial, until the post-trial visit
* Consumes greater than 3 glasses of alcoholic beverages (1 glass is approximately equivalent to: beer \[354 mL/12 ounces\], wine \[118 mL/4 ounces\], or distilled spirits \[29.5 mL/1 ounce\]) per day. Participants who consume 4 glasses of alcoholic beverages per day may be enrolled
* Consumes excessive amounts, defined as greater than 6 servings (1 serving is approximately equivalent to 120 mg of caffeine) of coffee, tea, cola, energy-drinks, or other caffeinated beverages per day
* Excessive smoker (i.e., more than 10 cigarettes/day) and is unwilling to restrict smoking to ≤10 cigarettes per day
* Cardiac QTc interval ≥470 msec (for males) or ≥480 msec (for females)
* Positive urine drug screen (except for cannabis) at screening and/or predose; rechecks are allowed
* Is or has an immediate family member (e.g., spouse, parent/legal guardian, sibling or child) who is investigational site or Sponsor staff directly involved with this trial.