We study feature selection (support recovery) in sparse linear models, including linear and logistic regression, under a strong adversarial contamination model where an adversary can arbitrarily corrupt a constant fraction of samples in the high-dimensional regime. We propose a trimmed maximum likelihood estimator with l1-regularization, leading to a non-convex relaxation of an NP-hard combinatorial optimization problem, and prove near-minimax statistical rates up to logarithmic factors.