Fano resonance appears for conduction through an electron waveguide containing donor impurities. In this work, we consider the thin-film conducting chiral helimagnet (CCH) as the donor impurity in a one-dimensional waveguide model. The transmission and conductance for an arbitrary CCH spiral period are obtained. Due to the spin-spiral coupling, interference between the direct and inter-subband transmission channels gives rise to a spin-dependent Fano resonance effect. The spin-dependent Fano resonance is sensitively dependent on the helicity of the spiral. By tuning the CCH potential well depth and the incident energy, this provides a potential way to detect the spin-spiral period in the CCH.