  Chiral spin-triplet superconductivity is a topologically nontrivial pairing
state with broken time-reversal symmetry, which can host Majorana
quasiparticles. The recently discovered heavy-fermion superconductor UTe$_2$
exhibits peculiar properties of spin-triplet pairing, and the possible chiral
state has been actively discussed. However, the symmetry and nodal structure of
its order parameter in the bulk, which determine the Majorana surface states,
remains controversial. Here we focus on the number and positions of
superconducting gap nodes in the ground state of UTe$_2$. Our magnetic
penetration depth measurements for three field orientations in the Meissner
state reveal the power-law temperature dependence with exponents nearly equal
to 2 or less than 2, which excludes single-component spin-triplet states. The
anisotropy of low-energy quasiparticle excitations indicates multiple point
nodes near the $k_y$- and $k_z$-axes, evidencing that the order parameter has
multiple components in a chiral complex form. We find that most consistent is a
chiral $B_{3u}+iA_u$ non-unitary state, which provides fundamentals of the
topological properties in UTe$_2$.
