I will present Chandra ACIS-I and ACIS-S observations ( ~ 200 ks in total) of the X-ray luminous elliptical galaxy NGC 4636, located in the outskirts of the Virgo cluster. A soft band (0.5-2 keV) image shows the presence of a bright core in the center surrounded by an extended X-ray corona and two pronounced quasi-symmetric, 8 kpc long, arm-like features. Each of this features defines the rim of an ellipsoidal bubble. An additional bubble-like feature, whose northern rim is located ~ 2 kpc south of the north-eastern arm, is detected as well. I will present surface brightness and temperature profiles across the rims of the bubbles, showing that their edges are sharp and characterized by temperature jumps of about 20-25 %. Through a comparison of the observed profiles with theoretical shock models, I will demonstrate that a scenario where the bubbles were produced by shocks, probably driven by energy deposited off-center by jets, is the most viable explanation to the X-ray morphology observed in the central part of NGC 4636. As a confirmation to this scenario, radio jets extending towards the bubbles and a central weak X-ray and radio source are detected and are most likely the signs of AGN activity which was more intense in the past. A bright dense core of ~ 1 kpc radius is observed at the center of NGC 4636. A sharp decline in surface brightness from the core to the ambient gas is observed and is not accompanied by a variation in the temperature and thus could not be in thermal pressure equilibrium. However the bright core could be a long lived feature if the radio jets are acting as a balancing factor to thermal pressure or if the bright core is produced by steep abundance gradients.