For linear colliders, extremely small and stable beam is required for high luminosity. At ILC (International Linear Collider), designed vertical beam size and required vertical position stability at the interaction point is nanometer level. For confirming feasibility of such small and stable beam, a prototype of the final focus system of ILC was constructed as an extension of ATF (Accelerator Test Facility) at KEK. This uses small emittance beams produced in and extracted from the damping ring of ATF. The project of final focus system study is called ATF2. One of the most important issues in squeezing beam is chromatic aberration, aberration caused by energy spread of beam. We have demonstrated the local chromatic correction method, which will be used for ILC, and observed the vertical beam size about 44 nm with low intensity beam.