We present three-dimensional numerical magnetohydrodynamic simulations of radiatively inefficient spherical accretion onto a black hole. The simulations are initialized with a Bondi Ñow and with a weak, dynamically unimportant, large-scale magnetic Ðeld. As the gas Ñows in, the magnetic Ðeld is ampliÐed. When the magnetic pressure approaches equipartition with the gas pressure, the Ðeld begins to reconnect and the gas is heated up. The heated gas is buoyant and moves outward, causing line stretching of the frozen-in magnetic Ðeld. This leads to further reconnection and more heating and buoyancy-induced motions, so that the Ñow makes a transition to a state of self-sustained convection. The radial structure of the Ñow changes dramatically from its initial Bondi proÐle, and the mass accretion rate onto the black hole decreases signiÐcantly. Motivated by the numerical results, we develop a simpliÐed analytical model of a radiatively inefficient spherical Ñow in which convective transport of energy to large radii plays an important role. In this "" convection-dominated Bondi Ñow,ÏÏ the accretion velocity is highly subsonic, and the density varies with radius as o P R~1@2 rather than the standard Bondi scaling o P R~3@2. We estimate that the mass accretion rate onto the black hole correspondingly scales as M 0 D where is a small multiple of the Schwarzschild radius of the black hole and is theaccretion radius ÏÏ at which the ambient gas in the surrounding medium is gravitationally captured by the black hole. Since the factor is typically very small, is signiÐcantly less than the Bondi R in /R a M 0 accretion rate. Convection-dominated Bondi Ñows may be relevant for understanding many astrophysical phenomena, e.g., post-supernova fallback and radiatively inefficient accretion onto supermassive black holes, stellar-mass black holes, and neutron stars.