Modern Hindi and neighboring languages employ structures with the present participle plus `be' as unmarked present, and structures with a form of rahnā `remain' as progressive present. This differs from Sanskrit and early Middle Indo-Aryan which have an undifferentiated simple present and optional structures with participles indicating continuous action, and also from late Middle Indo-Aryan (Apabhraṁśa) in which an innovated, marked progressive (present participle plus `be') contrasts with the old simple present. I present evidence and arguments in favor of a drag-chain explanation, first adumbrated by Bloch (1920). I demonstrate that the old simple present changed to modal (or future) in almost all of Modern Indo-Aryan, as the result of a marking reversal by which the late Middle-Indo-Aryan progressive becomes unmarked (as in English) and the old simple present becomes marked perfective and hence incompatible with present tense. I show that different languages fill the resulting gap in different ways. The fact that Hindi and related languages choose the earlier progressive structure for this purpose in turn motivates the use of an older, marked, continuative construction with rahnā to fill the resulting gap. Chain shifts, thus, are not limited to phonology but can also occur in morphology.