There is cross-linguistic variation in how speakers process ambiguous relative clauses (RCs) (e.g., The girl saw the maid “NP1” of the princess “NP2” who was eating chocolate). English speakers, for example, prefer to interpret the RC (e.g., who was eating chocolate) as modifying the second noun phrase (the princess; low attachment), whereas Spanish and Modern Standard Arabic speakers prefer to interpret the RC as modifying the first noun phrase (the maid; high attachment) (e.g., Bidaoui et al., 2016; Dussias, 2003). The present study examined the RC attachment preference in monolingual speakers and second-language (L2) learners in two offline interpretation experiments. Experiment 1 tested the RC attachment preference in Najdi Arabic monolinguals, revealing a preference for the first noun phrase (i.e., high attachment) in their interpretation of Najdi Arabic ambiguous RCs. These results are consistent with Gibson et al.’s (1996) claim that the principle of Predicate Proximity is more likely to override the universal principle of Recency in languages that permit greater distances between the verb and its complements. Experiment 2 tested the RC attachment preference in Najdi Arabic learners of English. Unlike English speakers, Najdi Arabic learners of English preferred the first noun phrase (i.e., high attachment) when interpreting ambiguous English RCs, indicating a transfer of RC attachment preference from their L1 to their L2. These results challenge the Shallow Structure Hypothesis, which argues against L1 transfer of structure-based processing principles (e.g., Predicate Proximity) and posits that L2 learners are restricted to shallow processing that relies more on semantic cues than on syntactic cues.