Gene transfection is a valuable tool for analyzing gene regulation and function, and providing an avenue for the genetic engineering of cells for therapeutic purposes. Though efficient, the potential concerns over viral vectors for gene transfection has led to research in non-viral alternatives. Cationic polyplexes such as those synthesized from chitosan offer distinct advantages such as enhanced polyplex stability, cellular uptake, endo-lysosomal escape, and release, but are limited by the poor solubility and viscosity of chitosan. In this study, the easily synthesized biocompatible and biodegradable polymeric polysorbate 80 polybutylcyanoacrylate nanoparticles (PS80 PBCA NP) are utilized as the backbone for surface modification with chitosan, in order to address the synthetic issues faced when using chitosan alone as a carrier. Plasmid DNA (pDNA) containing the brain-derived neurotrophic factor (BDNF) gene coupled to a hypoxia-responsive element and the cytomegalovirus promotor gene was selected as the genetic cargo for the in vitro transfection-guided neural-lineage specification of mouse induced pluripotent stem cells (iPSCs), which were assessed by immunofluorescence staining. The chitosan-coated PS80 PBCA NP/BDNF pDNA polyplex measured 163.8 ± 1.8 nm and zeta potential measured −34.8 ± 1.8 mV with 0.01% (w/v) high molecular weight chitosan (HMWC); the pDNA loading efficiency reached 90% at a nanoparticle to pDNA weight ratio of 15, which also corresponded to enhanced polyplex stability on the DNA stability assay. The HMWC-PS80 PBCA NP/BDNF pDNA polyplex was non-toxic to mouse iPSCs for up to 80 μg/mL (weight ratio = 40) and enhanced the expression of BDNF when compared with PS80 PBCA NP/BDNF pDNA polyplex. Evidence for neural-lineage specification of mouse iPSCs was observed by an increased expression of nestin, neurofilament heavy polypeptide, and beta III tubulin, and the effects appeared superior when transfection was performed with the chitosan-coated formulation. This study illustrates the versatility of the PS80 PBCA NP and that surface decoration with chitosan enabled this delivery platform to be used for the transfection-guided differentiation of mouse iPSCs.