Causal inference often relies on the counterfactual framework, which requires\nthat treatment assignment is independent of the outcome, known as strong\nignorability. Approaches to enforcing strong ignorability in causal analyses of\nobservational data include weighting and matching methods. Effect estimates,\nsuch as the average treatment effect (ATE), are then estimated as expectations\nunder the reweighted or matched distribution, P . The choice of P is important\nand can impact the interpretation of the effect estimate and the variance of\neffect estimates. In this work, instead of specifying P, we learn a\ndistribution that simultaneously maximizes coverage and minimizes variance of\nATE estimates. In order to learn this distribution, this research proposes a\ngenerative adversarial network (GAN)-based model called the Counterfactual\n$\\chi$-GAN (cGAN), which also learns feature-balancing weights and supports\nunbiased causal estimation in the absence of unobserved confounding. Our model\nminimizes the Pearson $\\chi^2$ divergence, which we show simultaneously\nmaximizes coverage and minimizes the variance of importance sampling estimates.\nTo our knowledge, this is the first such application of the Pearson $\\chi^2$\ndivergence. We demonstrate the effectiveness of cGAN in achieving feature\nbalance relative to established weighting methods in simulation and with\nreal-world medical data.\n