Dative alternation between prepositional and double object datives has been a popular topic in second language (L2) acquisition, but only few studies deal with discourse constraints such as the "given-before-new" principle, or given-new (GN) ordering, which describes the tendency to place given information before new information. The present study investigated Chinese English as a Foreign Language (EFL) learners at different proficiency levels on their ability to instantiate the GN order in English dative constructions to account for their difficulty regarding the discourse constraint that is expected to stem from structural differences between the two languages. In this study, 140 Chinese EFL learners were divided into 4 groups according to their proficiency levels, with ten native speakers in the control group. In a written elicited production task, six dative verbs were presented both in the given-theme and the given-recipient conditions so that the alignment of two objects and the errors in their responses could be probed. Results demonstrated that sensitivity to the GN principle tended to increase as the participants' English proficiency increased. More specifically, the GN order is more frequently instantiated in prepositional datives so that learners with high proficiency behave similar to native speakers while even advanced learners have difficulty producing as much GN order in double object datives as native speakers. A combination of two factors concerning the type of dative constructions and information structures is suggested to account for the results. Additionally, it was observed that Chinese learners of English would rather drop the given argument than produce new-given (NG) order, which violates the GN principle, probably due to their first language (L1) allowing topic drop.