Background: The genetic basis of variation in the progression of primary tauopathies has not been determined. We aimed to identify genetic determinants of survival in progressive supranuclear palsy (PSP). Methods: In stage one of this two stage genome-wide association study (GWAS), we included individuals with PSP, diagnosed according to pathological and clinical criteria, from two separate cohorts: the 2011 PSP GWAS cohort, from brain banks based at the Mayo Clinic (Jacksonville, FL, USA) and in Munich (Germany), and the University College London PSP cohort, from brain banks and the PROSPECT study, a UK-wide longitudinal study of patients with atypical parkinsonian syndromes. Individuals were included if they had clinical data available on sex, age at motor symptom onset, disease duration (from motor symptom onset to death or to the date of censoring, Dec 1, 2019, if individuals were alive), and PSP phenotype (with reference to the 2017 Movement Disorder Society criteria). Genotype data were used to do a survival GWAS using a Cox proportional hazards model. In stage two, data from additional individuals from the Mayo Clinic brain bank, which were obtained after the 2011 PSP GWAS, were used for a pooled analysis. We assessed the expression quantitative trait loci (eQTL) profile of variants that passed genome-wide significance in our GWAS using the Functional Mapping and Annotation of GWAS platform, and did colocalisation analyses using the eQTLGen and PsychENCODE datasets. Findings: Data were collected and analysed between Aug 1, 2016, and Feb 1, 2020. Data were available for 1001 individuals of white European ancestry with PSP in stage one. We found a genome-wide significant association with survival at chromosome 12 (lead single nucleotide polymorphism rs2242367, p=7·5 × 10−10, hazard ratio 1·42 [95% CI 1·22–1·67]). rs2242367 was associated with survival in the individuals added in stage two (n=238; p=0·049, 1·22 [1·00–1·48]) and in the pooled analysis of both stages (n=1239; p=1·3 × 10−10, 1·37 [1·25–1·51]). An eQTL database screen revealed that rs2242367 is associated with increased expression of LRRK2 and two long intergenic non-coding RNAs (lncRNAs), LINC02555 and AC079630.4, in whole blood. Although we did not detect a colocalisation signal for LRRK2, analysis of the PSP survival signal and eQTLs for LINC02555 in the eQTLGen blood dataset revealed a posterior probability of hypothesis 4 of 0·77, suggesting colocalisation due to a single shared causal variant. Interpretation: Genetic variation at the LRRK2 locus was associated with survival in PSP. The mechanism of this association might be through a lncRNA-regulated effect on LRRK2 expression because LINC02555 has previously been shown to regulate LRRK2 expression. LRRK2 has been associated with sporadic and familial forms of Parkinson's disease, and our finding suggests a genetic overlap with PSP. Further functional studies will be important to assess the potential of LRRK2 modulation as a disease-modifying therapy for PSP and related tauopathies. Funding: PSP Association, CBD Solutions, Medical Research Council (UK).