The best I can offer is what I sent to ecl.
Under the black coating, is the chrome shiny or does it appear to be sanded?

If you want to refinish it your self do these steps.

With spray paint (good quality) and a clear coat spray.
1. I used one of the adapters to prep all the stubbys. or find a threaded bolt that you can chuck in a drill.
2. spin the antenna and sand the chrome with 100 grit. get the grooves also.
3. use some acetone or alcohol to clean the surface real good.
4. coat the antenna with 3 light coats of spray paint if done that way.
5. warm the antenna to help bond the spray paint to about 200 degrees.
6. Let cool.
7. spray 3 light coats of the clear spray.
8. Again warm the antenna to help with the bonding of the paint, let cool and install back on your HHR.

With ProTec Powder Paint.
1. I used one of the adapters to prep all the stubbys. or find a threaded bolt that you can chuck in a drill.
2. spin the antenna and sand the chrome with 100 grit. get the grooves also.
3. use some acetone or alcohol to clean the surface real good.
4. I pre-heated the antenna with a hot air blower warm, not hot.
5. Spin the antenna with the drill and dip it into the powder paint and remove.
6. warm the antenna with the hot air blower. With the powder paint it is around 300-350 degrees or until the powder coat turns shiny.
7. If you end up with excess powder coat paint on the antenna, spin the antenna while its hot and remove all the paint, Did mine with a pocket knife, then start back at step 2..

It took me a few times to get it right so the spray method may work better for you.
If you want the powder coat feel free to send it to me, I wish I could guarantee them but only some of them are having the paint chip off and that where the salt areas are mostly. I sent some free ones out early on but I have no more to send. The rust issue was from the vendor putting a cheep chrome on.

Hope this helps.