Stromules are dynamic thin protrusions of membrane envelope from plant cell plastids. Despite considerable progress in understanding the importance of certain cytoskeleton elements and motor proteins for stromule maintenance, their function within the cell has yet to be unraveled. Several viruses cause a remodulation of plastid structures and stromule biogenesis within their host plants. For RNA-viruses these interactions were demonstrated to be relevant to the infection process. An involvement of plastids and stromules is assumed in the DNA-virus life cycle as well, but their functional role needs to be determined. Recent findings support a participation of heat shock cognate 70 kDa protein (cpHSC70-1)-containing stromules induced by a DNA-virus infection (Abutilon mosaic virus, AbMV, Geminiviridae) in intra- and intercellular molecule exchange. The chaperone cpHSC70-1 was shown to interact with the AbMV movement protein (MP). Bimolecular fluorescence complementation confirmed the interaction of cpHSC70-1 and MP, and showed a homo-oligomerization of either protein in planta. The complexes were detected at the cellular margin and co-localized with plastids. In healthy plant tissues cpHSC70-1-oligomers occurred in distinct spots at chloroplasts and in small filaments extending from plastids to the cell periphery. AbMV-infection induced a cpHSC70-1-containing stromule network that exhibits elliptical dilations and transverses whole cells. Silencing of the cpHSC70 gene revealed an impact of cpHSC70 on chloroplast stability and restricted AbMV movement, but not viral DNA accumulation. Based on these data, a model is suggested in which these stromules function in molecule exchange between plastids and other organelles and perhaps other cells. AbMV may utilize cpHSC70-1 for trafficking along plastids and stromules into a neighboring cell or from plastids into the nucleus. Experimental approaches to investigate this hypothesis are discussed.