The London penetration depth, $lambda(T)$, has been measured in several single crystals of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$. Thermodynamic, electromagnetic, and structural characterization measurements confirm that these crystals are of excellent quality. The observed low temperature variation of $lambda(T)$ follows a power-law, $Delta lambda (T) sim T^n$ with $n=2.4 pm 0.1$, indicating the existence of normal quasiparticles down to at least $0.02T_c$. This is in contrast to recent penetration depth measurements on single crystals of NdFeAsO$_{1-x}$F$_x$ and SmFeAsO$_{1-x}$F$_x$, which indicate an anisotropic but nodeless gap. We propose that a more three-dimensional character in the electronic structure of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$ may lead to an anisotropic $s-$wave gap with point nodes that would explain the observed $lambda(T)$.
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