Twisting is a prevalent feature of long, thin vertical leaves; it has been shown that this twist contributes to the mechanical integrity of the leaf. We address the question as to how this twist comes about, and posit that it is a reflection of twist at a lower structural (geometric) level. The stiffness required for maintaining verticality in leaves is due to turgescent parenchyma cells, sometimes thickened epidermis, cuticle, and is generally most significantly contributed to by vascular bundles and fibers. These contain cellulose in the cell walls. Such cellulose chains spiral upward within the cell wall layers which are of a characteristic handedness. This results in an isolated cell behaving mechanically in a chiral manner; specifically elongation (contraction) of a single cell will result in rotation of the cell about its axis of particular handedness. We propose a mathematical model that shows that when cells are mechanically associated in groups, the chiral behavior of the cell will be expressed at larger scales, albeit to a mitigated degree. Thus cell extension during leaf development may explain the characteristic twist of such leaves.