Chaos enables randomness-based applications, particularly in photonic systems. Integrated optical frequency combs (microcombs) have previously been observed in either chaotic modulation instability or stable, low-noise dissipative Kerr soliton (DKS) regimes. In this work, we demonstrate a new microcomb state where a single DKS exhibits chaotic behavior. By phase modulating the Kerr-induced synchronization (KIS) between a DKS and an externally injected reference laser, we observe chaotic group velocity hopping of the soliton, causing random transitions of the repetition rate. Using a chip-integrated octave-spanning microcomb, we experimentally validate the second-order Adler equation describing KIS, allowing us to predict and demonstrate this chaotic DKS hopping. This work connects nonlinear dynamics with optical soliton physics, providing a deterministic framework for triggering microcomb chaos in the solitonic state.