Fast object tracking on embedded devices is of great importance for applications such as autonomous driving, unmanned aerial vehicle, and intelligent monitoring. Whereas, most of previous general solutions failed to reach this goal due to the facts that (i) high computational complexity and heterogeneous operation steps in the tracking models and (ii) parallelism-limited and bloated hardware platforms (e.g., CPU/GPU). Although previously proposed devices leverage neural dynamics and near-data processing for efficient tracking, their flexibility is limited due to the tight integration with vision sensor and the effectiveness on various video datasets is yet to be fully demonstrated. On the other side, recently the many-core architecture with massive parallelism and optimized memory locality is being widely applied to improve the performance for flexibly executing neural networks. This motivates us to adapt and map an object tracking model based on attractor neural networks with continuous and smooth attractor dynamics onto neural network chips for fast tracking. In order to make the model hardware friendly, we add local-connection restriction. We analyze the tracking accuracy and observe that the model achieves comparable results on typical video datasets. Then, we design a many-core neural network architecture with several computation and transformation operations to support the model. Moreover, by discretizing the continuous dynamics to the corresponding discrete counterpart, designing a slicing scheme for efficient topology mapping, and introducing a constant-restricted scaling chain rule for data quantization, we build a complete mapping framework to implement the tracking model on the many-core architecture. We fabricate a many-core neural network chip to evaluate the real execution performance. Results show that a single chip is able to accommodate the whole tracking model, and a fast tracking speed of nearly 800 FPS (frames per second) can be achieved. This work enables high-speed object tracking on embedded devices which normally have limited resources and energy.