888-598-7978

Received an error message on my iMac, telling me to call this number (purportedly Apple Support)....I want to know whether it's legitimate or not.  This number is not listed on the Apple site.

This is a very well known scam & there are lots of reports of it on this site. I assume you are using the safari web browser. You need to clear its cache. You can do a web search yourself, but here's what Apple has to say & do to fix the problem. Whatever you do - DO NOT! phone that phone number!:
https://discussions.apple.com/docs/DOC-8071

Total scam, the number belongs to Spurtek, in Plano, TX, a UPS store address. They want all your payment information to fix your computer after receiving their pop up.