Experiments with graphene have demonstrated that 2D van der Waals materials can be stable, robust, and efficiently manipulated at the level of individual atomic planes. However, the stability and manipulation of 1D van der Waals materials and individual atomic chains remains elusive. Here, the ability to exfoliate and process two representative van der Waals materials containing 1D motifs, namely MoI3 and Ta2Se8I, at the scale of individual atomic chains is demonstrated. High-resolution transmission electron microscopy and atomic force microscopy studies confirm the presence of stable individual atomic chains of MoI3 at room temperature. It is further shown that 1D van der Waals materials with low exfoliation energy, such as Ta2Se8I, can be processed with electron beams to achieve suspended individual atomic chains. Ab initio calculations corroborate the findings regarding the cleavage energies and the thermodynamic stability of individual atomic chains in these 1D van der Waals materials. These results demonstrate that the top-down approach in material processing can be extended to the scale of individual chains.