Due to fundamental limitations, the progressing miniaturization of electronic components will soon come to an end. To fulfil the ever-growing demand of higher bandwidth and memory, radically new computations methods are required. A solution to this dilemma is quantum computation and quantum information processing. This is a radically new paradigm of information processing that employs quantum features as superposition and entanglement to greatly enhance the calculation power and to provide functionalities beyond those of a classical device. Among the different types of physical realization of quantum information carriers, so called quantum bits (qubits), photons are one of the most promising candidates. They are well decoupled from their environment, but can easily be manipulated and integrated into optical circuits. Furthermore, they can be transported over large distances in optical fibres and are thus directly compatible with modern communication infrastructures. However, a direct photon-photon interaction does not exist in free space, and thus creating a two-photon gate remains a challenge. Here, we propose to implement a deterministic photon-photon universal quantum gate, mediated by the interaction of an atom strongly coupled to a resonator. In particular, we take advantage of the recently discovered chiral nature of the photons in micro-nanophotonics waveguides structures, which enables us to realize a quantum gate in a fully integrated environment.