A good multivitamin with C, E, Selenium, zinc and others is a good idea during chelating.
I recommend you supplement Iodine
as well. I've had trouble with my thyroid which went away when I started using a little iodized salt everyday (a bit more if the thyroid symptoms seemed worse than usual). This problem was especially acute while using ALA. Be careful with Iodine
since it can be harmful if you consume too much.