I was logged into iNaturalist.ca. As @cthawley cthawley noted above, the “Add a new place” option does not appear there. In order to create a place, I had to log into iNaturalist.com (which I had never done before).
I have not been able to successfully create a new place yet because the gateway times out every time I have tried to save one. But I will try again in the next few days and see if it works if I try to do it at a different time of day when iNat has less traffic.