The Gitter API requires you to retrieve a token to have access to the entire API. You can follow this tutorial to get a token using OAuth2 authentication.
Now, you should receive a token. All you need to do is to provide it to the ApiService :
IGitterApiService gitterApiService = new GitterApiService();
gitterApiService.Token = "the-token";
In case you want to set the token instantly by creating a new instance of GitterApiService, you can use a specific constructor :
IGitterApiService gitterApiService = new GitterApiService("the-token");
Be careful, you need to set the token each time you create a new instance of GitterApiService.
Moreover, I've created another project / NuGet package that you can use to do authentication easily. You can retrieve this package following the GitHub repository here : https://github.com/Odonno/gitter-api-auth.