I wouldn’t be too concerned about cracking, I would be worried about the paint adhering to the Varnish. Sanding it first would give the paint a rough service to stick to, but that may be a lot of work depending on the style of chair. I have used a product called “Super Primer” made by General Paint here in Canada. It sticks very well to surfaces that most paints and primers will not (glass, plastic and other high gloss surfaces). I even primed bare aluminum patio furniture. If you put a primer like this on, you might save yourself some grief. Put your finish paint coat over top of the primer.