We present a new variational theory of chemical reaction rates. The theory, called improved canonical variational theory (ICVT), provides a bound on the classical mechanical equilibrium reaction rate. As compared to canonical variational theory (the method of free-energy curves) it involves a more accurate treatment of the threshold region. Classically the method consists of eliminating all contributions to the generalized transition-state theory rate constant from energies below the energetic reaction threshold and then estimating the contribution from the remaining truncated canonical ensemble by variational optimization of a generalized transition state dividing surface in configuration space. The ICVT is illustrated and tested by applications to classical collinear reaction rates in several systems. We also provide tests of the unified statistical theory for two new reactions.