We report the first direct measurements of superfluid density, n s (T) λ -2 (T), in films of Fepnictide superconductors. The magnetic penetration depth, λ(0), in our epitaxial, single-crystal Ba(Co x Fe 1-x ) 2 As 2 films near optimal doping (x=0.08) is 350 nm to 430 nm, comparable to bulk single crystals. The T-dependence of -2 indicates a small s-wave gap, 2Δ(0)/k B T c = 2.2 ± 0.1. In detail, has power-law behavior at low T: λ(T)/(0) -1 0.60*(T/T c ) 2.5±0.1 . The small gap, together with power-law behavior at low T, suggests strong intraband scattering on the largergap Fermi surface and significant interband scattering between large-gap and small-gap Fermi surfaces.