Microscopic chirality is not at all necessary to explain curly hair (or other objects). All that is required is flexibility. Once hair gets long enough, it collides with itself, and is pushed off to one side or another, forming a chiral curl.
For some anecdotal evidence against microscopic chirality, find someone with large diameter hanging curls in their hair. Those seem to often curl straight back on to themselves. A more compelling anecdote is that curled objects, including hair and telephone cords (if anyone still remembers those) can be pulled through themselves and chirally inverted. Sometimes there will be some resistance, but that could be the keratin or plastic or whatever having set in its shape over time, rather than being preferentially formed that way.
These are obviously both anecdotal though, and the idea that there is some slight chiral preference isn't ruled out. I'm not even opposed to the fundamental idea of transitive chirality through several orders of superhelicity (look at DNA), but it just hasn't been my empirical experience. As Ryan points out, if it were a strong effect, all hair would curl the same way, and straight hair wouldn't exist at all.
Just to provide a bit of data, this paper demonstrates that hair curvature is based on the distribution of 4 different cell types in a follicle. The keratin (and many other proteins associated with) intermediate fibrils were associated with curvature, but only to the extend that their compositions were different in the 4 cell types. But the curvature was based on the distribution of the cells themselves. Chirality wasn't specifically studied in the paper, but I think (given that they were staring at individual fibers with an electron microscope) that they would have noticed it had it existed.
Cortical cell types and intermediate filament arrangements correlate with fiber curvature in Japanese human hair
Naturally straight and curved human scalp hairs were examined using fluorescence and electron microscopy techniques to determine morphological and ultrastructural features contributing to single fiber curvature. The study excluded cuticle and medulla, which lack known bilateral structural asymmetry and therefore potential to form curved fibers. The cortex contained four classifiable cell types, two of which were always present in much greater abundance than the remaining two types. In straight hair, these cell types were arranged annularly and evenly within the cortex, implying that the averaging of differing structural features would maintain a straight fiber conformation. In curved fibers, the cell types were bilaterally distributed approximately perpendicular to fiber curvature direction with one dominant cell type predominantly located closest to the convex fiber side and the other, closest to the concave side. Electron tomography confirmed that the dominant cell type closest to the convex fiber side contained discrete macrofibrils composed of helically arranged intermediate filaments, while the dominant cell type closest to the concave side contained larger fused macrofibrils composed of intermediate filament arrangements varying from helical to hexagonal arrays approximately parallel to the longitudinal fiber axis. These findings concur with the current hypothesis of hair curvature formation and behavior.