Quantum computers promise ultrafast performance for certain tasks(1). Experimentally appealing, measurement-based quantum computation(2) requires an entangled resource called a cluster state(3), with long computations requiring large cluster states. Previously, the largest cluster state consisted of eight photonic qubits(4) or light modes(5), and the largest multipartite entangled state of any sort involved 14 trapped ions(6). These implementations involve quantum entities separated in space and, in general, each experimental apparatus is used only once. Here, we circumvent this inherent inefficiency by multiplexing light modes in the time domain. We deterministically generate and fully characterize a continuous-variable cluster state(7,8) containing more than 10,000 entangled modes. This is, by three orders of magnitude, the largest entangled state created to date. The entangled modes are individually addressable wave packets of light in two beams. Furthermore, we present an efficient scheme for measurement-based quantum computation on this cluster state based on sequential applications of quantum teleportation.