I am in the process of rewiring a chandelier to lengthen the chain. I have wired it using a single strand of the insulated lamp wire as the ground - is this safe/ok to do instead of using the exposed copper wiring I typically see for the ground?

Sure, identify both ends with green tape.
Personally, I like going in and out of every other link, seems to look good, pull slack in wire so chain supports the weight, not the wires.

Thanks for the quick reply and information.
I figured that wiring trick out last night - but only after first stringing it through with the chandelier on the ground, then when I did a dry run of hanging it the chain looked terrible! I then hung the chain from the ceiling and ran the wire through while it was hanging with the weight of the chandelier keeping the chain tight and it looked 200% better :)