Protoclusters of galaxies have been found in the last quarter-century. However, most of them have been found through the overdensity of star-forming galaxies, and there have been no known structures identified by more than two spectroscopically confirmed quiescent galaxies at z > 2.5. In this letter, we report the discovery of an overdense structure of massive quiescent galaxies with the spectroscopic redshift z = 2.77 in the COSMOS field, QO-1000. We first photometrically identify this structure as a 4.2 sigma overdensity with 14 quiescent galaxies in 7 x 4 pMpc(2 )from the COSMOS2020 catalog. We then securely confirm the spectroscopic redshifts of four quiescent galaxies by detecting multiple Balmer absorption lines with Keck/MOSFIRE. All the spectroscopically confirmed members are massive (log (M-* M-?) > 11.0) and located in a narrow redshift range (2.76 < z < 2.79). Moreover, three of them are in the 1 x 1 pMpc(2) in the transverse direction at the same redshift (z = 2.760-2.763). Such a concentration of four spectroscopically confirmed quiescent galaxies implies that QO-1000 is > 68 times denser than the general field. In addition, we confirm that they form a red sequence in the J - Ks color. This structure's halo mass is estimated as log(M-halo M-?) > 13.2 from its stellar mass. Similar structures found in the IllustrisTNG simulation are expected to evolve into massive galaxy clusters with log(M-halo M-?) >= 14.8 at z = 0. These results suggest that QO-1000 is a more mature protocluster than the other known protoclusters. It is likely in a transition phase between star-forming protoclusters and quenched galaxy clusters.