We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2 + 1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16(3) x 48 lattice at a lattice spacing similar to 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the epsilon regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in (2 + 1)-flavor QCD with strange quark mass fixed at its physical value as Sigma((MS) over bar)(2 GeV) = [242(04)(+ 19 -18) MeV](3) where the errors are statistical and systematic, respectively.