  Single crystalline samples of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with $x < 0.12$
have been grown and characterized via microscopic, thermodynamic and transport
measurements. With increasing Co substitution, the thermodynamic and transport
signatures of the structural (high temperature tetragonal to low temperature
orthorhombic) and magnetic (high temperature non magnetic to low temperature
antiferromagnetic) transitions are suppressed at a rate of roughly 15 K per
percent Co. In addition, for $x \ge 0.038$ superconductivity is stabilized,
rising to a maximum $T_c$ of approximately 23 K for $x \approx 0.07$ and
decreasing for higher $x$ values. The $T - x$ phase diagram for
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ indicates that either superconductivity can
exist in both low temperature crystallographic phases or that there is a
structural phase separation. Anisotropic, superconducting, upper critical field
data ($H_{c2}(T)$) show a significant and clear change in anisotropy between
samples that have higher temperature structural phase transitions and those
that do not. These data show that the superconductivity is sensitive to the
suppression of the higher temperature phase transition.
