Do HubSpot APIs support CORS / AJAX requests?

At this time, HubSpot APIs do not support support cross-origin (CORS) AJAX requests. Making the request client-side would expose any authentication you're using for the request. In order to use AJAX, you would need to make the request (excluding any authentication) to an external server that could then add the needed authentication and make requests to HubSpot's APIs server-side.

For example, if you wanted to submit form data to the Forms API using AJAX, you would need to send that request to an external server, process it server-side, and post to HubSpot's endpoint from that external server.