The formation of galaxies by gradual hierarchical co-assembly of baryons and cold dark matter halos is a fundamental paradigm underpinning modern astrophysics[1, 2] and predicts a strong decline in the number of massive galaxies at early cosmic times[3–5]. Extremely massive quiescent galaxies (stellar masses > 1011M⊙) have now been observed as early as 1–2 billions years after the Big Bang[6–13]; these are extremely constraining on theoretical models as they form 300–500 Myr earlier and only some models can form massive galaxies this early [12, 14]. Here we report on the spectroscopic observations with the James Webb Space Telescope of a massive quiescent galaxy ZF-UDS-7329 at redshift 3.205 ± 0.005 that eluded deep ground-based spectrscopy[8], is significantly redder than typical and whose spectrum reveals features typical of much older stellar populations. Detailed modelling shows the stellar population formed around 1.5 billion years earlier in time (z ~ 11) at an epoch when dark matter halos of sufficient hosting mass have not yet assembled in the standard scenario[4, 5]. This observation may point to the presence of undetected populations of early galaxies and the possibility of significant gaps in our understanding of early stellar populations, galaxy formation and/or the nature of dark matter.