Here, we explore the possibility of creating DFTB models that can leverage the relative simplicity of linear regression machine learning in the recently developed Chebyshev Interaction Model for Efficient Simulation (ChIMES) method. ChIMES is a many-body force field based on linear combinations of Chebyshev polynomials. It has been shown that ChIMES models yield good agreement with DFT reference method for a wide range of properties and materials under both ambient and extreme conditions. The main advantage of ChIMES is that it is completely linear in fitted coefficients, allowing for rapid parameterization to a global minimum. The reliance on Chebyshev polynomials, which are orthogonal, allows the complexity of a ChIMES model to be systematically tuned to an arbitrary degree of accuracy and transferability, while also providing straightforward methods for regularization to minimize overfitting. In this study, we determine an optimal DFTB/ChIMES model for C, H, N, O-containing systems using high level quantum chemical reference data. We use an iterative scheme to systematically expand our training set where at each iteration, a small fraction of the force configurations with largest deviation in our validation set are included in the next training set iteration. The accuracy and transferability of the resulting model are investigated for a wide variety of gas-phase clusters as well as some carbon solids. We find that use of a small fraction of our chosen data set (∼0.3% of similar NN efforts) yields DFTB/ChIMES models that maintain close to hybrid functional, coupled-cluster, and/or experimental accuracy for the gas-phase clusters studies here, and compares favorably to previous DFTB-NN efforts for similar systems.