The electromagnetic field theory for a step-index fiber geometry is developed to sense a surrounding chiral drug via long-period fiber gratings (LPFGs). This theory employs Debye potentials and electromagnetic fields for cladding modes in the LPFGs by introducing constitutive relations for a chiral drug. The fields in the chiral drug are transformed and decomposed into right- and left-hand circularly polarized components to account for the magnetoelectric coupling due to the chirality. The solving process for complex propagation constants is given. Numerical results show that responses of the LPFGs to refractive index and chirality changes are different. The two minimum transmissions of a coated LPFG are very sensitive to the variation of the complex chirality. On the other hand, the two resonance wavelengths keep invariant as real and imaginary parts of the comparatively small chirality change. This work enriches the electromagnetic field theory for better design of LPFGs against the highly sensitive chirality detection.