A population of faint, old, and massive quiescent galaxies at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3

Here we present a sample of 12 massive quiescent galaxy candidates at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z\sim 3-4$$\end{document}z∼3-4 observed with the James Webb Space Telescope (JWST) Near Infrared Spectrograph (NIRSpec). These galaxies were pre-selected from the Hubble Space Telescope imaging and 10 of our sources were unable to be spectroscopically confirmed by ground based spectroscopy. By combining spectroscopic data from NIRSpec with multi-wavelength imaging data from the JWST Near Infrared Camera (NIRCam), we analyse their stellar populations and their formation histories. We find that all of our galaxies classify as quiescent based on the reconstruction of their star formation histories but show a variety of quenching timescales and ages. All our galaxies are massive (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 0.1-1.2\times 10^{11}$$\end{document}∼0.1-1.2×1011 M⊙), with masses comparable to massive galaxies in the local Universe. We find that the oldest galaxy in our sample formed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 1.0\times 10^{11}$$\end{document}∼1.0×1011 M⊙ of mass within the first few hundred million years of the Universe and has been quenched for more than a billion years by the time of observation at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z\sim 3.2$$\end{document}z∼3.2 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 2$$\end{document}∼2 billion years after the Big Bang). Our results point to very early formation of massive galaxies requiring a high conversion rate of baryons to stars in the early Universe.