Adaptive phenotypic plasticity in chemical defense is thought to play a major role in plant-herbivore interactions. We investigated genetic variation for inducibility of defensive traits in wild radish plants and asked if the evolution of induction is constrained by costs of phenotypic plasticity. In a greenhouse experiment using paternal half-sibling families, we show additive genetic variation for plasticity in glucosinolate concentration. Genetic variation for glucosinolates was not detected in undamaged plants, but was significant following herbivory by a specialist herbivore, Pieris rapae. On average, damaged plants had 55% higher concentrations of glucosinolates compared to controls. In addition, we found significant narrow-sense heritabilities for leaf size, trichome number, flowering phenology, and lifetime fruit production. In a second experiment, we found evidence of genetic variation in induced plant resistance to P. rapae. Although overall there was little evidence for genetic correlations between the defensive and life-history traits we measured, we show that more plastic families had lower fitness than less plastic families in the absence of herbivory (i.e., evidence for genetic costs of plasticity). Thus, there is genetic variation for induction of defense in wild radish, and the evolution of inducibility may be constrained by costs of plasticity.