We introduce Discriminative BLEU (deltaBLEU), a novel metric for intrinsic evaluation of generated text in tasks that admit a diverse range of possible outputs. Reference strings are scored for quality by human raters on a scale of [-1, +1] to weight multi-reference BLEU. In tasks involving generation of conversational responses, deltaBLEU correlates reasonably with human judgments and outperforms sentence-level and IBM BLEU in terms of both Spearmans rho and Kendalls tau.