We present the first discovery of brown dwarfs in a globular cluster with confirmed cluster membership. We identified three substellar members with effective temperatures between 1300 and 1800 K in the JWST NIRCam images of the globular cluster NGC 6397. The membership of these objects was verified with proper motion selection, using archival HST data. We employed a new set of model isochrones with non-solar abundances, computed across the stellar/substellar transition, to confirm that the discovered objects have masses well below the hydrogen-burning limit. The long-term cooling of brown dwarfs allows the ages of parent populations to be estimated from the observed luminosity function of the substellar sequence. Using this technique, we calculated the age of NGC 6397 as 13.4 ± 3.3 Gyr. Based on the cluster age determined by us and other estimates in the literature, we conclude that the newly discovered substellar members of NGC 6397 are likely the oldest known brown dwarfs with reliable age measurements. Theme(s): New Insights into Star Formation and Evolution, Brown Dwarfs and Giant Exoplanets: Future Prospects and Thirty Years of Discovery Associated publication: Gerasimov et al. 2024 [ADS]