<p>The deterministic and stochastic control of nonlinear dynamics in magnetic solitons is crucial for future information processing technologies. Yet, the transition to chaos in such systems remains largely unexplored. Here, we demonstrate that a confined magnetic vortex, when driven by a rotating in-plane magnetic field under low excitation, follows well-defined trochoidal trajectories in its core motion. We classify these trajectories using a trochoidal constant that captures the competition between the intrinsic gyrotropic frequency and the frequency of the external drive. This parameter determines both the rotational symmetry of the orbit and the number of core-trajectory revolutions required for closure. Beyond a critical excitation threshold, the underlying trochoidal symmetry breaks down, giving rise to a vortex-core reversal process that evolves into fully chaotic dynamics. We construct a dynamic phase diagram identifying distinct regimes of locked, quasi-periodic, and chaotic reversals. Importantly, the vortex core functions as a field-driven binary oscillator with extreme sensitivity to initial conditions, enabling deterministic yet unpredictable switching behavior. Our findings reveal a mechanism of driving-induced chaotic dynamics in topological magnetic textures, with potential applications in unconventional computing platforms such as stochastic spintronic logic devices.</p>