Bound states in the continuum (BICs) garnered significant interest for their potential to create new types of nanophotonic devices. Most prior demonstrations were based on arrays of dielectric resonators, which cannot be miniaturized beyond the diffraction limit, reducing the applicability of BICs for advanced functions. Here, we demonstrate BICs and quasi-BICs based on highquality factor phonon-polariton resonances in isotopically pure h 11 BN and how these states can be supported by periodic arrays of nanoresonators with sizes much smaller than the wavelength. We theoretically illustrate how BICs emerge from the band structure of the arrays and verify both numerically and experimentally the presence of these states and enhanced quality factors. Furthermore, we identify and characterize simultaneously quasi-BICs and bright states. Our method can be generalized to create a large number of optical states and to tune their coupling with the environment, paving the way to miniaturized nanophotonic devices with more advanced functions.