We present results for the first three low-power radio galaxi es from the B2 bright sample to have been observed with Chandra. Two have kpc-scale radio jets, and in both Chandra resolves jet X-ray emission, and detects soft X-ray core emission and an X-ray emitting galaxy-scale atmosphere of luminosity a few 10 41 ergs s 1 . These are the first detections of X-ray jets in low-power radio galaxies more distant than Cen A and M 87. The cooling time of the galaxy-scale gas implies mass infall rates of order on e solar mass per year. The gas pressure near the jets is comparable to the minimum pressure in the jets, implying that the X-ray emitting gas may play an important role in jet dynamics. The third B2 radio galaxy has no kpc-scale radio jet, and here only soft X-ray emission from the core is detected. The ratio of X-ray to radio flux is similar for the jets and cores, and the results favour a synchrotron origin for the emission. kpc-scale radio jets are detected i n the X-ray in � 7 ks exposures with Chandra more readily than in the optical via HST snapshot surveys.