If you're pulling off the clear coat, you may want to use an X-Acto knife to cut the clear coat at the demarcation between the chrome and paint. This will reduce the probability of pulling off some paint with the clear coat, as the clear coat will adhere better to paint than the paint to the chrome. However, the cut increases the probability of corrosion, so ensure this area is well sealed afterwards.

Also, I've seen cases where the chromium itself has peeled, exposing the nickel. However, in this case, the effect is the opposite, with the exposed nickel being duller and slightly yellow.