We present the first results from a 500 ks Chandra ACIS-I observation of M87. At soft energies (0.5-1.0 keV), we detect filamentary structures associated with the eastern and southwestern X-ray and radio arms. Many filaments are spatially resolved with widths of similar to 300 pc. This filamentary structure is particularly striking in the eastern arm, where we suggest the filaments are outer edges of a series of plasma-filled, buoyant bubbles whose ages differ by similar to 6 x 10 super(0) yr. These X-ray structures may be influenced by magnetic filamentation. At hard energies (3.5-7.5 keV), we detect a nearly circular ring of outer radius 2.8' (13 kpc), which provides an unambiguous signature of a weak shock, driven by an outburst from the supermassive black hole (SMBH). The density rise in the shock is rho sub(shock) rho sub(o) approximately 1.3 (Mach number, M approximately 1.2). The observed spectral hardening in the ring corresponds to a temperature rise T sub(shock)/T sub(o) unk 1.2, or M approximately 1.2, in agreement with the Mach number derived independently from the gas density. Thus, for the first time, we detect gas temperature and density jumps associated with a classical shock in the atmosphere around a SMBH. We also detect two additional surface brightness edges and pressure enhancements at radii of similar to 0.6' and similar to 1'. The similar to 0.6' feature may be overpressurized thermal gas surrounding the relativistic plasma in the radio cocoon, the "piston," produced by the current episode of AGN activity. The overpressurized gas is surrounded by a cool gas shell. The similar to 1' feature may be an additional weak shock from a secondary outburst. In an earlier episode, the piston was responsible for driving the 2.8' shock.