  We present Chandra ACIS-I and ACIS-S observations ($\sim$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 rimof an ellipsoidal bubble. An additional bubble-like feature, whose
northern rim is located $\sim2$ kpc south of the north-eastern arm, is detected
as well. We 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, we 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.
