Electrospun hybrid scaffolds composed of synthetic and natural polymers have gained increasing interest in tissue engineering applications over the last decade. In this work, scaffolds composed of polylactic acid electrospun fibers, either treated (P-PLA) or non-treated (PLA) with air-plasma, were coated with high molecular weight chitosan to create a core-shell microfibrous structure. The effective thickness control of the chitosan layer was confirmed by gravimetric, spectroscopic (FTIR-ATR) and morphological (SEM) investigations. The chitosan coating increased the fiber diameter of the microfibrous scaffolds while the tensile mechanical tests, conducted in dry and wet environments, showed a reinforcing action of the coating layer on the scaffolds, in particular when deposited on P-PLA samples. The stability of the Chi coating on both PLA and P-PLA substrates was confirmed by gravimetric analysis, while their mineralization capacity was evaluated though scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS) after immersing the scaffolds in simulated body fluids (SBF) at 37 °C for 1 week. Sample biocompatibility was investigated through cell viability assay and SEM analysis on mouse pre-osteoblastic MC3T3-E1 cells grown on scaffolds at different times (1, 7, 14 and 21 days). Finally, Alizarin Red assay and qPCR analysis suggested that the combination of plasma treatment and chitosan coating on PLA electrospun scaffolds influences the osteoblastic differentiation of MC3T3-E1 cells, thus demonstrating the great potential of P-PLA/chitosan hybrid scaffolds for bone tissue engineering applications.