Further power scaling of narrow-linewidth fiber lasers is critical for beam combining. Using all-solid photonic bandgap fibers with large effective mode areas and strong higher-order-mode suppression is an interesting approach. Previously, we demonstrated ∼400W single-frequency single-mode power at 1064 nm from a 50/400 photonic bandgap fiber amplifier, limited only by transverse mode instability (TMI). In this work, we demonstrate a TMI-limited single-mode power of 1.37 kW from a monolithic fiber amplifier with a 25/400 photonic bandgap fiber, the highest output power from a photonic bandgap fiber demonstrated to date, to the best of our knowledge. The spectral linewidth is broadened to ∼8GHz to suppress stimulated Brillouin scattering.