We consider the obstacle problem for stable-like operators with uniformly bounded, symmetric, and Lipschitz continuous jump kernels. We establish existence and uniqueness of solutions when the obstacle function $\varphi\in C_c^{2,1}​(\mathbb{R}^d)$. Using blow-up analysis together with Mosco convergence, we classify the blow-up limits arising from the limiting obstacle problem. We prove that the free boundary is locally Lipschitz and can be further improved to $C^{1,\gamma}$ regularity. In addition, we establish the optimal regularity of solutions, namely $C^{1,\alpha/2}$. This is a joint work with Zhen-Qing Chen.