Single crystals of BaFe_2As_2 and (Ba_0.55K_0.45)Fe_2As_2 have been grown out of excess Sn with 1 crystals are exceptionally micaceous, are easily exfoliated and can have dimensions as large as 3 x 3 x 0.2 mm^3. The BaFe_2As_2 single crystals manifest a structural phase transition from a high temperature tetragonal phase to a low temperature orthorhombic phase near 85 K and do not show any sign of superconductivity down to 1.8 K. This transition can be detected in the electrical resistivity,

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... l resistivity, specific heat and the anisotropic magnetic susceptibility. In the (Ba_0.55K_0.45)Fe_2As_2 single crystals this transition is suppressed and instead superconductivity occurs with a transition temperature near 30 K. Whereas the superconducting transition is easily detected in resistivity and magnetization measurements, the change in specific heat near T_c is small, but resolvable, giving Δ C_p/γ T_c ≈ 1. The application of a 140 kOe magnetic field suppresses T_c by only ∼ 4 K when applied along the c-axis and by ∼ 2 K when applied perpendicular to the c-axis. The ratio of the anisotropic upper critical fields, γ = H_c2^ c / H_c2^ c, varies between 2.5 and 3.5 for temperatures down to ∼ 2 K below T_c.