Poly(lactic acid)-cellulose nanocrystals (PLA/CNC) nanocomposite fibers with 1% weight fraction of nanocrystals were prepared by melt-spinning. In order to improve the compatibility between the 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, thermal and mechanical properties of the fibers with different draw ratios were evaluated. The results of this research show that the surface modification together with drawing resulted in improved fiber properties, which is expected to depend on the alignment of the CNC and of the PLA molecular chains. The modification is also expected to lead to a flexible interface which also leads to more stretchable fibers. The main conclusion is that PLLA grafting is a very promising way to improve the dispersion of CNC in PLA, creating an interfacial adhesion between the phases and making possible to spun fibers which can be drawn with improved mechanical performance.