Photonic quantum technologies such as quantum cryptography, photonic quantum metrology, photonic quantum simulators and computers will largely benefit from highly scalable and small footprint quantum photonic circuits. To perform fully on-chip quantum photonic operations, three basic building blocks are required: single-photon sources, photonic circuits and single-photon detectors. Highly integrated quantum photonic chips on silicon and related platforms have been demonstrated incorporating only one or two of these basic building blocks. Previous implementations of all three components were mainly limited by laser stray light, making temporal filtering necessary or required complex manipulation to transfer all components onto one chip. So far, a monolithic, simultaneous implementation of all elements demonstrating single-photon operation remains elusive. Here, we present a fully-integrated Hanbury-Brown and Twiss setup on a micron-sized footprint, consisting of a GaAs waveguide embedding quantum dots as single-photon sources, a waveguide beamsplitter and two superconducting nanowire single-photon detectors. This enables a second-order correlation measurement at the single-photon level under both continuous-wave and pulsed resonant excitation.