In previous work on undoped MFe(2)As(2), partial drops in the resistivity indicative of traces of superconductivity have been observed for some samples with M = Ba (T(c)∼20 K, up to 25% drop in ρ) and M = Ca (T(c)∼10 K, up to 45% drop in ρ). A complete drop in the resistivity to ρ = 0, along with a finite fraction of Meissner flux expulsion, has been observed for M = Sr, T(c) = 22 K. Using In-flux grown single crystal samples of undoped BaFe(2)As(2), we find a complete drop in the resistivity to 0 for most samples beginning at T(c)(onset) = 22.5 K. However-in contrast to the SrFe(2)As(2) results-there is no measurable Meissner effect and no suppression of the resistive superconducting transition with annealing. The current sensitivity of the superconducting resistive transition in our samples of BaFe(2)As(2) is quite strong, with an increase in the current density of a factor of 15 to ∼1.5 A cm(-2) not changing T(c)(onset) but broadening the transition significantly and causing ρ to remain finite as [Formula: see text]. To investigate whether this unusually low critical current is indicative of filamentary conduction lacking the apparent anisotropy seen in the critical magnetic field, H(c2), measurements for, e.g., the bulk superconductor Co-doped BaFe(2)As(2), H(c2) was measured in both crystalline directions. These BaFe(2)As(2) samples show H(c2)(T) values in the ab-plane and along the c-axis comparable to those seen for BaFe(2-x)Co(x)As(2), which has a similar T(c). Since the lack of T(c) suppression after annealing argues against strain-induced superconductivity as proposed for the other undoped MFe(2)As(2) materials, another possible cause for the superconductivity in BaFe(2)As(2) is discussed.