High-temperature superconductivity often emerges in the proximity of a symmetry-breaking ground state. For superconducting iron arsenides, in addition to the antiferromagnetic ground state, a small structural distortion breaks the crystal's C(4 )rotational symmetry in the underdoped part of the phase diagram. We reveal that the representative iron arsenide Ba(Fe(1)(-x)Co(x))(2)As(2) develops a large electronic anisotropy at this transition via measurements of the in-plane resistivity of detwinned single crystals, with the resistivity along the shorter b axis rho(b) being greater than rho(a). The anisotropy reaches a maximum value of ~2 for compositions in the neighborhood of the beginning of the superconducting dome. For temperatures well above the structural transition, uniaxial stress induces a resistivity anisotropy, indicating a substantial nematic susceptibility.