To elucidate the nature of the superconducting ground state of the geometrically frustrated pyrochlore KOs2O6 (T-c=9.6 K), the thermal conductivity was measured down to low temperatures (similar to T-c/100). We found that the quasiparticle mean free path is strikingly enhanced below a transition at T-p=7.8 K, indicating enormous electron inelastic scattering in the normal state. In magnetic fields, the conduction at T -> 0 K is nearly constant up to similar to 0.4H(c2), in contrast with the rapid growth expected for superconductors with an anisotropic gap. This unambiguously indicates a fully gapped superconductivity, in contrast with previous studies. These results highlight that KOs2O6 is unique among superconductors with strong electron correlations.