POST request with SSL to 3rd party API, failing: "Origin http://localhost:5000 is not allowed by Access-Control-Allow-Origin."

I'm developing a website with AngularJS and Restangular, and for the first time trying to send AJAX requests to a 3rd party webservice. Plus, it uses a SSL certificate.

The request is at the end of this message. It sends back an error 0, and displays in the console:

OPTIONS https://identitysso-strongauth.betfair.com/api/certlogin Origin http://localhost:5000 is not allowed by Access-Control-Allow-Origin. angular.min.js:100

and

XMLHttpRequest cannot load https://identitysso-strongauth.betfair.com/api/certlogin. Origin http://localhost:5000 is not allowed by Access-Control-Allow-Origin. 

I know this is a CORS situation. This is the browser not wanting to go and fetch information from this server. But I don't know how to make it work.

I tried to send a similar POST request with curl and it worked. One thing I had to do with curl, was to indicate where my SSL certificates were. Ah! Writing this, I thought that Chrome might need to know where the certificates are. I added them in the Settings. There was a change. Now, the request is "Pending" and never receives any response. There is no more error message in the console.

The request is pending forever... no idea what to do. I will keep on investigating, but if someone had an idea (or even a proposal of tool I could use to investigate), that would be very welcome as I am pretty much a beginner in these matters.

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And here is the request before and after setting the SSL certificate in Chrome:

Request URL:https://identitysso-strongauth.betfair.com/api/certlogin
Request Method:OPTIONS
Status Code:200 OK
Request Headersview source
Accept:*/*
Accept-Encoding:gzip,deflate,sdch
Accept-Language:en-US,en;q=0.8,fr;q=0.6
Access-Control-Request-Headers:x-application, accept, origin, x-requested-with, content-type
Access-Control-Request-Method:POST
Cache-Control:no-cache
Connection:keep-alive
Host:identitysso-strongauth.betfair.com
Origin:http://localhost:5000
Pragma:no-cache
Referer:http://localhost:5000/
User-Agent:Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/29.0.1547.76 Safari/537.36

and after:

Request URL:https://identitysso-strongauth.betfair.com/api/certlogin
Request Headersview source
Access-Control-Request-Headers:x-application, accept, origin, x-requested-with, content-type
Access-Control-Request-Method:POST
Cache-Control:no-cache
Origin:http://localhost:5000
Pragma:no-cache
Referer:http://localhost:5000/
User-Agent:Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/29.0.1547.76 Safari/537.36

I have no idea why the request is not exactly the same, as my code is exactly the same.