To elucidate the nature of the superconducting ground state of the geometrically frustrated pyrochlore KOs2O6 (Tc=9.6 K), the thermal conductivity was measured down to low temperatures (approximately Tc/100). We found that the quasiparticle mean free path is strikingly enhanced below a transition at Tp=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 approximately 0.4Hc2, 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.