This paper studies semiparametric contextual bandits, a generalization of the linear stochastic bandit problem where the reward for an action is modeled as a linear function of known action features confounded by a non-linear action-independent term. We design new algorithms that achieve Õ(d√T) regret over T rounds, when the linear function is d-dimensional, which matches the best known bounds for the simpler unconfounded case and improves on a recent result of Greenewald et al. (2017). Via an empirical evaluation, we show that our algorithms outperform prior approaches when there are non-linear confounding effects on the rewards. Technically, our algorithms use a new reward estimator inspired by doubly-robust approaches and our proofs require new concentration inequalities for self-normalized martingales.