Textile chitosan fiber scaffolds were developed and tested in terms of biocompatibility for human bone marrow stromal cells (hBMSCs). A part of the scaffolds was further modified by coating with fibrillar collagen type I in order to biologize the surface. hBMSCs of two donors were used for cell culture experiments in vitro. Confocal laser scanning microscopy (CLSM) as well as scanning electron microscopy (SEM) revealed fast attachment and morphological adaptation of the cells on both the raw chitosan fibers and the collagen-coated scaffolds. Cells were osteogenically induced after 3 days and cultivated for up to 28 days on the scaffolds. Activity of lactate dehydrogenase (LDH) and alkaline phosphatase (ALP) was analyzed to evaluate proliferation as well as osteogenic differentiation. We found a 3.5-6-fold increase in the cell number, whereas the collagen coating did not noticeably influence these factors. Osteogenic differentiation was confirmed by the course of ALP activity and immunostaining of osteocalcin. The feature of the collagen-coated as well as the raw chitosan fiber scaffolds to support attachment, proliferation, and differentiation of hBMSCs suggests a potential application of chitosan fibers and textile chitosan scaffolds for the tissue engineering of bone.