Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of QCD they allow for variational calculations with non-Gaussian wave functionals: by means of DSEs the various $n$-point functions, needed in expectation values of observables like the Hamiltonian, can be expressed in terms of the variational kernels of the trial Ansatz for the vacuum wave functional. Equations of motion for these variational kernels are derived by minimizing the energy density, renormalized, and solved numerically. We determine the chiral condensate from the renormalized quark propagator.