Dolutegravir Study in HIV-1 Participants Completing IMPAACT Studies P1093 and P2019

Inclusion Criteria: * Participant must have completed participation in one of the following parent studies, for the duration noted, with continued benefit from investigational product: 1. P1093 parent study through at least Week 180; 2. P2019 parent study through at least Week 48. * Participant with evidence of Virological Failure in either parent study must have eligibility for this rollover study discussed and agreed with the ViiV Healthcare Medical Monitor. * Virological control: 1. Participants in parent study P1093 must have virological control defined as HIV-1 ribonucleic acid (RNA) \<400 copies per milliliter (c/mL) at their penultimate visit (on or after the Week 180 visit); 2. Participants in parent study P2019 must have virological control defined as HIV-1 RNA \<200 c/mL at their penultimate visit (on or after Week 36). * Evidence of continued benefit from IP during the subject's participation in the parent study (P1093 or P2019) 1. At screening, Investigators will submit a clinical summary verifying evidence of continued benefit from IP during the subject's participation in the parent study (P1093 or P2019). 2. The summary will be submitted via the PPD ePIP system to the Study Medical Monitor who will review and confirm if the inclusion criterion has been met. 3. Confirmation from the Study Medical Monitor is required to meet this eligibility criterion * Males and Females: All participants who are engaging in sexual activity should be counseled on safer sexual practices including the use and benefit/risk of effective barrier methods (example \[e.g.\] male condom) and on the risk of HIV transmission to an uninfected partner. Females: Female participants who are of child- bearing potential and who are engaging in sexual activity that could lead to pregnancy, must agree to use one of the acceptable birth control methods until the last dose of study medication and completion of the follow-up visit (4 weeks after the last dose). Condoms are recommended in addition, because their appropriate use is the only contraception method effective for preventing HIV-1 transmission. * Parent or legal guardian or participant \>=18 years of age is able and willing to provide signed informed consent. Exclusion Criteria: * Confirmed virologic failure with evidence of resistance to: 1. DTG in the P1093 parent study, or 2. ABC, DTG or 3TC (with the exception of M184V) in the P2019 parent study * Presence of any active AIDS defining opportunistic infection. * Known \>=grade 3 laboratory toxicities prior to study entry (e.g. neutrophil count, hemoglobin, platelets, aspartate aminotransferase \[AST\], alanine aminotransferase \[ALT\], lipase, serum creatinine and total bilirubin) would be considered exclusionary if identified at or after the penultimate parent study visit, prior to enrollment in the study... Repeat testing is allowed for eligibility determination. * Previous permanent discontinuation from investigational product in the parent study due to toxicity, intolerance or pregnancy. * Known ALT \>=5 times the upper limit of normal (ULN), or ALT \>=3 times ULN and bilirubin \>=1.5 times ULN (with \>35 percent \[%\] direct bilirubin) would be considered exclusionary if identified at or after the penultimate parent study visit, prior to enrolment in the study.. Participants with moderate to severe hepatic impairment (Class B or greater) as determined by Child-Pugh classification should be excluded. * Participants positive for hepatitis B virus at any time prior to entry (hepatitis B virus surface antigen positive). * Females who are pregnant or plan to become pregnant or breastfeed during the study. * Participant is currently participating in or has participated in a study with a compound or device that is not commercially available within 30 days of signing informed consent, unless permission from the sponsor's medical monitor is granted. * Presence of any history of allergy/sensitivity to any of the study drugs. * Participants transitioning from the P2019 study (taking ABC/DTG/3TC) have evidence of being Human Leukocyte Antigen-B\*5701- positive based on documented testing at any time prior to entry. * Use of any disallowed medications at time of Screening. * Anticipated need for Hepatitis C virus therapy with interferon or any drugs that have potential for adverse drug: drug interactions with study treatment throughout the entire study period. * Participant is unlikely to adhere to the study procedures, keep appointments, or is planning to relocate during the study. * Clinical or symptomatic evidence of pancreatitis, as determined by the clinician. * Any condition (including but not limited to alcohol and drug use) that would, in the opinion of the site investigator, place the participant at an unacceptable risk of injury or render the participant unable to meet the requirements of the protocol.