Fused deposition modeling (FDM) is currently the most popular 3D printing method, where thermoplastic polymers are predominantly used. Among them, the biobased poly(lactic acid) (PLA) governs the FDM filament market, with demand higher than supply, since not all grades of PLA are suitable for FDM filament production. In this work, the effect of a food grade chain extender (Joncryl ADR® 4400) on the physicochemical properties and printability of PLA marketed for injection molding was examined. All samples were characterized in terms of their mechanical and thermal properties. The microstructure of the filaments and 3D-printed fractured surfaces following tensile testing were examined with optical and scanning electron microscopy, respectively. Molecular weight and complex viscosity increased, while the melt flow index decreased after the incorporation of Joncryl, which resulted in filaments of improved quality and 3D-printed constructs with enhanced mechanical properties. Dielectric spectroscopy revealed that the bulk properties of PLA with respect to molecular mobility, both local and segmental, were, interestingly, not affected by the modifier. Indirectly, this may suggest that the major effects of the extender are on chain length, without inducing chain branching, at least not to a significant extent.