The London penetration depth lambda(T) has been measured in single crystals of Ba(Fe0.93Co0.07)2As2. The observed low-temperature variation of lambda(T) follows a power law, Deltalambda(T) approximately T(n) with n approximately 2.4+/-0.1, indicating the existence of normal quasiparticles down to at least 0.02T(c). This is in contrast with previous penetration depth measurements on single crystals of NdFeAsO1-xFx and SmFeAsO1-xFx, which indicate an anisotropic but nodeless gap. We discuss possible explanations of the observed power law behavior.