  Spin-triplet superconductors provide an ideal platform for realizing
topological superconductivity with emergent Majorana quasiparticles. The
promising candidate is the recently discovered superconductor UTe$ _2$, but the
symmetry of the superconducting order parameter remains highly controversial.
Here we determine the superconducting gap structure by the thermal conductivity
of ultra-clean UTe$ _2$ single crystals. We find that the $a$ axis thermal
conductivity divided by temperature $\kappa/T$ in zero-temperature limit is
vanishingly small for both magnetic fields $\mathbf{H}||a$ and $\mathbf{H}||c$
axes up to $H/H_{c2}\sim 0.2$, demonstrating the absence of any types of nodes
around $a$ axis contrary to the previous belief. The present results, combined
with the reduction of the NMR Knight shift in the superconducting state,
indicate that the superconducting order parameter belongs to the isotropic
$A_u$ representation with a fully gapped pairing state, analogous to the B
phase of superfluid $ ^3$He. These findings reveal that UTe$ _2$ is likely to
be a long-sought three-dimensional (3D) strong topological superconductor
characterized by a 3D winding number, hosting helical Majorana surface states
on any crystal plane.
