Unauthorized Error When Adding VSTS Private Feed Nuget Packages

I recently created a Nuget feed in VSTS to host some common packages that my company uses. These are all built with .NET Core. When we try to incorporate them into a new ASP.NET Core RC2 application, we get the following error:

error: Unable to load the service index for source https://[...]/nuget/v3/index.json.
error:   Response status code does not indicate success: 401 (Unauthorized).

.NET 4.6.1 packages sourced from the same feed which are added to an ASP.NET 4 application work just fine. Any ideas on what the problem might be?