  We present zero field and transverse field \muSR experiments on the recently
discovered electron doped Fe-based superconductor LaO_{1-x}F_xFeAs. The zero
field experiments on underdoped (x=0.075) and optimally doped (x=0.1) samples
rule out any static magnetic order above 1.6 K in these superconducting
samples. From transverse field experiments in the vortex phase we deduce the
temperature and field dependence of the superfluid density. Whereas the
temperature dependence is consistent with a weak coupling BCS s-wave or a dirty
d-wave gap function scenario, the field dependence strongly evidences
unconventional superconductivity. We obtain the in-plane penetration depth of
\lambda_{ab} (0) = 254(2)nm for LaO_{0.9}F_{0.1}FeAs and \lambda_{ab} (0) =
364(8)nm for LaO_{0.925}F_{0.075}FeAs. Further evidence for unconventional
superconductivity is provided by the ratio of T_c versus the superfluid
density, which is close to the Uemura line of hole doped high-T_c cuprates.
