We present a visual world eye-tracking study on Tseltal (a Mayan language) and investigate whether verbal information can be used to anticipate an upcoming referent. Basic word order in transitive sentences in Tseltal is Verb--Object--Subject (VOS). The verb is usually encountered first, making argument structure and syntactic information available at the outset, which should facilitate anticipation of the post-verbal arguments. Tseltal speakers listened to verb-initial sentences with either an object-predictive verb (e.g., "eat") or a general verb (e.g., "look for") (e.g., "Ya slo'/sle ta stukel on te kereme," "Is eating/is looking (for) by himself the avocado the boy/" "The boy is eating/is looking (for) an avocado by himself") while seeing a visual display showing one potential referent (e.g., avocado) and three distractors (e.g., bag, toy car, coffee grinder). We manipulated verb type (predictive vs. general) and recorded participants' eye movements while they listened and inspected the visual scene. Participants' fixations to the target referent were analyzed using multilevel logistic regression models. Shortly after hearing the predictive verb, participants fixated the target object before it was mentioned. In contrast, when the verb was general, fixations to the target only started to increase once the object was heard. Our results suggest that Tseltal hearers pre-activate semantic features of the grammatical object prior to its linguistic expression. This provides evidence from a verb-initial language for online incremental semantic interpretation and anticipatory processing during language comprehension. These processes are comparable to the ones identified in subject-initial languages, which is consistent with the notion that different languages follow similar universal processing principles.