Background Tuberous sclerosis complex is a genetic disorder leading to constitutive activation of mammalian target of rapamycin (mTOR) and growth of benign tumours in several organs. In the brain, growth of subependymal giant cell astrocytomas can cause life-threatening symptoms-eg, hydrocephalus, requiring surgery. In an open-label, phase 1/2 study, the mTOR inhibitor everolimus substantially and significantly reduced the volume of subependymal giant cell astrocytomas. We assessed the efficacy and safety of everolimus in patients with subependymal giant cell astrocytomas associated with tuberous sclerosis complex. Methods In this double-blind, placebo-controlled, phase 3 trial, patients (aged 0-65 years) in 24 centres in Australia, Belgium, Canada, Germany, the UK, Italy, the Netherlands, Poland, Russian Federation, and the USA were randomly assigned, with an interactive internet-response system, in a 2:1 ratio to oral everolimus 4·5 mg/m2 per day (titrated to achieve blood trough concentrations of 5-15 ng/mL) or placebo. Eligible patients had a definite diagnosis of tuberous sclerosis complex and at least one lesion with a diameter of 1 cm or greater, and either serial growth of a subependymal giant cell astrocytoma, a new lesion of 1 cm or greater, or new or worsening hydrocephalus. The primary endpoint was the proportion of patients with confirmed response-ie, reduction in target volume of 50% or greater relative to baseline in subependymal giant cell astrocytomas. Analysis was by intention to treat. This study is registered with ClinicalTrials.gov, number NCT00789828. Findings 117 patients were randomly assigned to everolimus (n=78) or placebo (n=39). 27 (35%) patients in the everolimus group had at least 50% reduction in the volume of subependymal giant cell astrocytomas versus none in the placebo group (difference 35%, 95% CI 15-52; one-sided exact Cochran-Mantel-Haenszel test, p<0·0001). Adverse events were mostly grade 1 or 2; no patients discontinued treatment because of adverse events. The most common adverse events were mouth ulceration (25 [32%] in the everolimus group vs two [5%] in the placebo group), stomatitis (24 [31%] vs eight [21%]), convulsion (18 [23%] vs ten [26%]), and pyrexia (17 [22%] vs six [15%]). Interpretation These results support the use of everolimus for subependymal giant cell astrocytomas associated with tuberous sclerosis. Additionally, everolimus might represent a disease-modifying treatment for other aspects of tuberous sclerosis.