  We study the linear Hall response of 2D ballistic system on inhomogeneous
magnetic field. We establish that in classical limit the Hall conductivity
response on local magnetic field is quantized in units of $\alpha_H \equiv
\frac{e^3}{2 \pi^2 \hbar c}$. The quantized value depends on the point where
the field is applied, this dependence being irregular in chaotic billiards. The
phenomenon allows for direct tracing of special electron trajectories that
belong to fractal repellor. We discuss how quantum effects smooth the
quantization.
