The expression of Hermite-Gaussian beam in terms of spherical vector wave functions is given with the complex source point method. Based on the generalized Lorenz-Mie theory, the scattering coefficients are obtained by applying the continuous boundary conditions of tangential components of electromagnetic field at the interface between chiral medium and free space. The scattering of Hermite-Gaussian beam by a chiral sphere is investigated. The angle distribution of far region scattering field by a chiral sphere located in the Hermite-Gaussian beam is numerically simulated. The influences of beam mode, chiral parameter and sphere radius on the scattering properties sections are analyzed in detail.