We report the first detection of a TeV 7-ray flux from the solar disk (6.3a), based on 6.1 years of data from the High Altitude Water Cherenkov (HAWC) observatory. The 0.5-2.6 TeV spectrum is well fit by a power law, dN/dE=A(E/1 TeV)-7, with A = (1.6 & PLUSMN; 0.3) x 10-12 TeV-1 cm-2 s-1 and 7 = 3.62 & PLUSMN; 0.14. The flux shows a strong indication of anticorrelation with solar activity. These results extend the bright, hard GeV emission from the disk observed with Fermi-LAT, seemingly due to hadronic Galactic cosmic rays showering on nuclei in the solar atmosphere. However, current theoretical models are unable to explain the details of how solar magnetic fields shape these interactions. HAWC's TeV detection thus deepens the mysteries of the solar-disk emission.