While I know that most modelers do remove the chrome, I and a few of my friends do not. As long as you use a decent primer, it works fine.
The chrome plating on plastic model parts is actually vapor deposited aluminum, so you want a primer that works well on aluminum. In the old days zinc chromate primer was the go-to for use with aluminum, but it was found to be carcinogenic and is extremely rare in small bottles or rattle cans. I have used auto body primers, like duplicolor, with chrome parts and always found it worked fine.