We present results from a Chandra observation of Abell 1060, the nearby cluster of galaxies. The ACIS-I image shows that the central cusp-like structure, previously seen from PSPC, is caused mainly by an emission from the central elliptical galaxy NGC 3311. We confirmed that the central region is remarkably isothermal with a temperature of 3.2 keV, based on the spectral fits for fine pixels. An extended region in the northeast of NGC 3311 indicates high iron abundance. The surface brightness profile excluding the central galaxy, NGC 3311, can be fitted only by a double beta model, with core radii about 40 and 140 kpc, out to a radius of about 200 kpc. This suggests that the gravitational potential in Abell 1060 consists of 2 components.