Systematic measurements of the resistivity, heat capacity, susceptibility, and Hall coefficient are presented for single-crystal samples of the electron-doped superconductor Ba(Fe1-xCox)(2)As-2. These data delineate an x-T phase diagram in which the single magnetic/structural phase transition that is observed for undoped BaFe2As2 at 134 K appears to split into two distinct phase transitions, both of which are rapidly suppressed with increasing Co concentration. Superconductivity emerges for Co concentrations above x similar to 0.025 and appears to coexist with the broken-symmetry state for an appreciable range of doping up to x similar to 0.06. The optimal superconducting transition temperature appears to coincide with the Co concentration at which the magnetic/structural phase transitions are totally suppressed, at least within the resolution provided by the finite-step size between crystals prepared with different doping levels. Superconductivity is observed for a further range of Co concentrations before being completely suppressed for x similar to 0.18 and above. The form of this x-T phase diagram is suggestive of an association between superconductivity and a quantum critical point arising from suppression of the magnetic and/or structural phase transitions.