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Single crystals of BaFe 2 As 2 and Ba 0.55 K 0.45 Fe 2 As 2 have been grown out of excess Sn with 1% or less incorporation of solvent. The crystals are exceptionally micaceous, are easily exfoliated, and can have dimensions as large as 3 ϫ 3 ϫ 0.2 mm 3 . The BaFe 2 As 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, Hall resistivity, specific heat, and the anisotropic magnetic susceptibility. In the Ba 0.55 K 0.45 Fe 2 As 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 ⌬C p / ␥T c Ϸ 1. The application of a 140 kOe magnetic field suppresses T c by only ϳ4 K when applied along the c axis and by ϳ2 K when applied perpendicular to the c axis. The ratio of the anisotropic upper critical fields, ␥ = H c2Ќc / H c2 ʈc , varies between 2.5 and 3.5 for temperatures down to ϳ2 K below T c .