High-flux polarized particle beams are of critical importance for the investigation of spin-dependent processes, such as in searches of physics beyond the Standard Model, as well as for scrutinizing the structure of solids and surfaces in material science. Here we demonstrate that kiloampere polarized electron beams can be produced via laser-wakefield acceleration from a gas target. A simple theoretical model for determining the electron beam polarization is presented and supported with self-consistent three-dimensional particle-in-cell simulations that incorporate the spin dynamics. By appropriately choosing the laser and gas parameters, we show that the depolarization of electrons induced by the laser-wakefield-acceleration process can be as low as 10%. Compared to currently available sources of polarized electron beams, the flux is increased by four orders of magnitude.