Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science(1). Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics(2), for increasing the sensitivity of quantum imaging schemes(3), for improving the robustness and key rate of quantum communication protocols(4), for enabling a richer variety of quantum simulations(5), and for achieving more efficient and error-tolerant quantum computation(6). Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states(7). However, so far, integrated entangled quantum sources have been limited to qubits (D = 2)(8-11). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.