A laser machining process is described for laser machining glass or glass-like materials. This process machines articles or features in articles with chamfered edges in one manufacturing operation. Chamfered edges are desirable in glass and glass-like materials because they resist fracturing or chipping and eliminate sharp edges. Producing articles or features in articles in one manufacturing operation is desirable because it can save time and expense by eliminating the need to transfer the article to a separate machine for chamfering after laser machining. Alternatively, it can permit use of less expensive equipment because the same laser used for machining can be used to form the chamfer instead of having a separate process perform the chamfering. Producing chamfers with laser machining results in high quality chamfers without the need for a separate polishing or finishing step.