Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet CrNb3S6 due to the specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to CrNb3S6, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded 2π kinks. The linear stability of these dark breather modes is verified by means of Floquet analysis. Their energy, which is controlled by two parameters, namely, the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a path to design spintronic resonators on the base of chiral helimagnets.