A vast body of research has proposed that Ancient Greek exhibits a fairly free word order, unconstrained by purely syntactic principles, and only determined by stylistic and expressive factors. Successive investigations have explored the possibility that at least a portion of the Ancient Greek clause structure conforms to already attested linguistic tendencies, according to various theoretical frameworks. This paper contributes to the debate by investigating a rather understudied clausal domain, namely the mood-tense-aspect portion of the clause structure (the so-called tense phrase, TP), with the help of a novel diagnostic, i.e. adverb placement. We argue that a hierarchical structure can be envisaged for the Classical Greek TP. We examine the position of the finite verb and the distribution of subject and object DPs in relation to the order of a series of temporal-aspectual adverbs. By adopting Cinque's adverb hierarchy, we show that the relative order of adverbs obeys the hierarchical structure proposed there for functional categories. If a fixed position for adverbs is assumed, as in Pollock (1989) and Cinque (1999), they can be used as markers to determine the position of other constituents in the clause, such as verbs and DPs. We then demonstrate that verb placement as well as the subject/object DP position with respect to various adverbs can be well accounted for within the cartographic model.