Chiral spin-triplet superconductivity is a topologically nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The heavy-fermion superconductor UTe2exhibits 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 UTe2. Our magnetic penetration depth measurements for three field orientations in three crystals all show the power-law temperature dependence with exponents close to 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near theky- andkz-axes in momentum space. These results can be consistently explained by a chiralB3u+iAunon-unitary state, providing fundamentals of the topological properties in UTe2.