This paper considers a new class of robust estimators in a linear instrumental variables (IV) model with many instruments. The estimators are generalized method of moments (GMM) estimators, and the class includes the limited maximum likelihood estimator (LIML) as a special case. Each estimator in the class is consistent and asymptotically normal under many instruments asymptotics, and this paper provides consistent variance estimators that are of the "sandwich" type and can be used to conduct asymptotically correct inference. Furthermore, this paper characterizes an optimal robust estimator among the members of the class. Compared to LIML, the optimal robust estimator is less influenced by outliers and more efficient under thick-tailed error distributions. In an empirical example (Angrist and Krueger, 1991), the optimal robust estimator is approximately 80% more efficient than LIML.