We propose a thresholding least-squares method for high-dimensional regression models when the number of parameters, p, tends to infinity with the sample size, n. We show that the thresholding least-squares estimator (TLSE) has the oracle property and that it is computationally efficient. We establish the oracle property of the TLSE when p=o(n), and that, under additional regularity conditions, the results continue to hold even if p=exp(o(n)). We show that, if properly centered, the residual bootstrap distribution of the TLSE is consistent, while a naive residual bootstrap is inconsistent. In a simulation study, we assess and compare the finite sample properties of the TLSE with LASSO-type estimators. The analysis of a real-world high-dimensional data set with a high degree of multicollinearity illustrates an application of the proposed method in practice.