Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2 exhibits magnetic order below T (N) = 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called 'stripe-yz' type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce-Ce bonds. No structural lattice distortions are revealed below T (N), indicating that the triangular lattice of Ce3+ ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results of ab initio calculations, and demonstrate that its magnetic ground state matches the experimental spin structure.