We construct a new Skyrme interaction Skχm^⁎ by fitting the equation of state and nucleon effective masses in asymmetric nuclear matter from chiral two- and three-body forces as well as the binding energies of finite nuclei. Employing this interaction to study the electric dipole polarizabilities of ⁴⁸Ca, ⁶⁸Ni, ¹²⁰Sn, and ²⁰⁸Pb in the random-phase approximation, we find that the theoretical predictions are in good agreement with experimentally measured values without additional fine tuning of the Skyrme interaction, thus confirming the usefulness of the new Skyrme interaction in studying the properties of nuclei. We further use this interaction to study the neutron skin thicknesses of ⁴⁸Ca and ²⁰⁸Pb, and they are found to be consistent with the experimental data.