Thin films of poly[2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene] (C(14)-PBTTT) exhibit a monolayer-terraced morphology that indicates a pronounced lamellar order with pi-stacks of extended polymer chains. Previously this remarkable state of order was thought to be promoted by the interdigitation of alkyl side chains between the lamellae during cooling from the liquid-crystalline (LC) phase. Here we establish that the key to this ordering in fact is the formation of unentangled pi-stacks of extended polymer chains in dilute solutions of chlorobenzene (CB) or 1,2-dichlorobenzene (o-DCB), which though routinely used as the "best" solvents are in fact borderline solvents. Film formation causes these pi-stacks to deposit substantially oriented in the film plane, while the subsequent anneal and cool from LC phase accentuates this incipient order to develop the monolayer-terraced morphology. This mechanism is supported by the following lines of evidence. (i) Hydrodynamic and viscometry measurements respectively of the Kuhn segment length and Mark-Houwink-Sakurada exponent of PBTTT reveal that CB is a near-Theta solvent, and PBTTT is significantly stiffer than regioregular polythiophene. (ii) Solution-state UV-vis spectroscopy reveals an early coil -> rod transition in highly dilute solutions, which gives rise to unentangled pi-stacks. (iii) Solid-state UV-vis spectroscopy, atomic force microscopy and variable-angle spectroscopic ellipsometry together reveal the as-deposited pi-stacks are already substantially oriented in the film plane. We further demonstrate that this monolayer-terraced morphology can also be induced in regioregular poly(3-hexylthiophene) films using a borderline solvent mixture of chlorobenzene and mesitylene, and in very dilute CB where the incipient pi-stacks do not entangle. Therefore, this dilute pi-stacking mechanism is general. Processing with a borderline solvent or solvent additive thus provides a general route to obtain superior supramolecular order in pi-stackable conjugated polymers.