We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.