Poly(lactic acid)-cellulose nanocrystals (PLA/CNC) nanocomposite fibers with 1% weight fraction of nanocrystals were prepared via melt-spinning. In order to improve the compatibility between PLA and the CNC, PLLA chains were grafted onto the CNC surface using a "grafting from" reaction. For comparison, melt-spun PLA fibers and nanocomposites with unmodified CNC were also prepared. The morphology and thermal and mechanical properties of the fibers with different draw ratios were determined. The results of this research show that the surface modification together with drawing resulted in improved fiber properties, which are expected to depend on the alignment of the CNC and PLA molecular chains. The modification is also expected to lead to a flexible interface, which leads to more stretchable fibers. The main conclusion is that PLLA grafting is a very promising approach to improve the dispersion of CNC in PLA, thus creating interfacial adhesion between the phases and making it possible to spin fibers that can be drawn with improved mechanical performance.