Background: In patients co-infected with HIV and tuberculosis, antiretroviral therapy options are limited due to drug-drug interactions with rifampicin. A previous phase 2 trial indicated that raltegravir 400 mg twice a day or efavirenz 600 mg once a day might have similar virological efficacy in patients given rifampicin. In this phase 3 trial, we assessed the non-inferiority of raltegravir to efavirenz. Methods: We did a multicentre, open-label, non-inferiority, randomised, phase 3 trial at six sites in Côte d'Ivoire, Brazil, France, Mozambique, and Vietnam. We included antiretroviral therapy (ART)-naive adults (aged ≥18 years) with confirmed HIV-1 infection and bacteriologically confirmed or clinically diagnosed tuberculosis who had initiated rifampicin-containing tuberculosis treatment within the past 8 weeks. Using computerised random numbers, we randomly assigned participants (1:1; stratified by country) to receive raltegravir 400 mg twice daily or efavirenz 600 mg once daily, both in combination with tenofovir and lamivudine. The primary outcome was the proportion of patients with virological suppression at week 48 (defined as plasma HIV RNA concentration <50 copies per mL). The prespecified non-inferiority margin was 12%. The primary outcome was assessed in the intention-to-treat population, which included all randomly assigned patients (excluding two patients with HIV-2 infection and one patient with HIV-1 RNA concentration of <50 copies per mL at inclusion), and the on-treatment population, which included all patients in the intention-to-treat population who initiated treatment and were continuing allocated treatment at week 48, and patients who had discontinued allocated treatment due to death or virological failure. Safety was assessed in all patients who received at least one dose of the assigned treatment regimen. Findings: Between Sept 28, 2015, and Jan 5, 2018, 460 participants were randomly assigned to raltegravir (n=230) or efavirenz (n=230), of whom 457 patients (230 patients in the raltegravir group; 227 patients in the efavirenz group) were included in the intention-to-treat analysis and 410 (206 patients in the raltegravir group; 204 patients in the efavirenz group) in the on-treatment analysis. At baseline, the median CD4 count was 103 cells per μL and median plasma HIV RNA concentration was 5·5 log10 copies per mL (IQR 5·0-5·8). 310 (68%) of 457 participants had bacteriologically-confirmed tuberculosis. In the intention-to-treat population, at week 48, 140 (61%) of 230 participants in the raltegravir group and 150 (66%) of 227 patients in the efavirenz had achieved virological suppression (between-group difference -5·2% [95% CI -14·0 to 3·6]), thus raltegravir did not meet the predefined criterion for non-inferiority. The most frequent adverse events were HIV-associated non-AIDS illnesses (eight [3%] of 229 patients in the raltegravir group; 21 [9%] of 230 patients in the efavirenz group) and AIDS-defining illnesses (ten [4%] patients in the raltegravir group; 13 [6%] patients in the efavirenz group). 58 (25%) of 229 patients in raltegravir group and 66 (29%) of 230 patients in the efavirenz group had grade 3 or 4 adverse events. 26 (6%) of 457 patients died during follow-up: 14 in the efavirenz group and 12 in the raltegravir group. Interpretation: In patients with HIV given tuberculosis treatment, non-inferiority of raltegravir compared with efavirenz was not shown. Raltegravir was well tolerated and could be considered as an option, but only in selected patients.