Neutron and x-ray diffraction studies show that the simultaneous first-order transition to an orthorhombic and antiferromagnetic (AFM) ordered state in BaFe2As2 splits into two transitions with Co doping. For Ba(Fe0.953Co0.047)2As2, a tetragonal-orthorhombic transition occurs at TS=60 K, followed by a second-order transition to AFM order at TN=47 K. Superconductivity occurs in the orthorhombic state below TC=17 K and coexists with AFM. Below TC, the static Fe moment is reduced along with a redistribution of low energy magnetic excitations indicating competition between coexisting superconductivity and AFM order.