I have an app in my salesforce developer account that I want to allow my users to access from a remote app that I am building. I see that I must use OAuth2.0 to first author
You will need to handle the OAUTH part on your own server. This isn't just due to lack of CORS, there is also no way to securely OAUTH purely on the client-side. The server could really be anything but here is an example server written in Java using Play Framework which has a JavaScript / AngularJS client as well: http://typesafe.com/activator/template/reactive-salesforce-rest-javascript-seed