We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, the symmetry gets promoted to a quantum group gauge symmetry. The theory depends on two parameters: the deformation parameter λ and the lattice spacing a. We show that the system of Kogut and Susskind is recovered when λ → 0, while QCD is recovered in the continuum limit (for any λ). We, thus, have the possibility of having a two-parameter regularization of QCD.