cookie error when mapping domain

I have the exact same problem described here: https://wordpress.org/support/topic/cookie-error-when-logging-after-changing-domain/

I have a multisite install. I created a new site. Everything is fine until I pick the domain I’ve bought for it, and then I can’t log in. I have another site on that install with its own domain (http://climbtothestars.org) and can log in fine.

What is the fix? It must be something simple, as the site works without the domain mapping and domain mapping works on another site of the same install.

Help!

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