This problem should be resolved in .NET Framework 5 and I've found several articles on how to incorporate "Nightly ASP.NET Build" feature into your existing Web API service. I'm not really comfortable with that and it can be hard to get it working properly.
All you have to do to fix this issue is add a few lines to your web.config under the system.webServer:
1: <system.webServer>
2: <httpProtocol>
3: <customHeaders>
4: <add name="Access-Control-Allow-Origin" value="*"/>
5: </customHeaders>
6: </httpProtocol>
7: <system.webServer>