Glass strength question

I have a piece of art glass in which a small chip has been made on an edge a few millimeters wide, and there is no “crack” – will this eventually destroy the item?

Probably not. When you say “eventually”, I take it you are concerned that a crack could grow and become long enough to greatly weaken the material. If the chip looks like it’s getting worse, there may be residual stresses in the glass that are making the crack grow. If the chip or crack isn’t currently getting any bigger, it will take repeated loading to make it start growing, so unless you move or shake your piece of art a lot, there won’t be any repeated load. I guess there is an outside chance that changes in temperature could make the crack expand and contract, which could be bad especially if water got in and froze, but that seems unlikely for a piece of art on a shelf.