The spin-1/2 kagome Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu3(OH)6Cl2, which unfortunately suffers from the notorious orphan spin problem caused by magnetic disorders. Here, we turn to YCu3(OH)6.5Br2.5, recently recognized as another host of a globally undistorted kagome Cu2+ lattice free from orphan spins, and thus a more feasible system for studying the intrinsic kagome quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishingly small residual linear term of κ/T (T→0), and thus clearly rule out itinerant gapless fermionic excitations. An unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a Z2 quantum spin liquid ground state. Additionally, an analysis of the magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.