Download a file from a Claims auth based SharePoint 2010 site programmatically

Question

I have a console application to download a file from a SharePoint site. The sharepoint site uses claims based authentication.

This code throws a 403 Forbidden exception. The specified Network credential has full access to the site, and is able to download the same file from a browser.

WebClient webClient = new WebClient();
webClient.Credentials = new NetworkCredential(username,Password,domain);
byte[] fileData = webClient.DownloadData(urlOfAFile); 
FileStream file = File.Create(localPath);
file.Write(fileData, 0, fileData.Length);

Any idea how to fix this?