How to authenticate with Twitter API 1.1 and Scribe?

Question

I'm trying to pull a timeline from my own twitter account in to a website using Scribe. I tried the provided Twitter example, but I'm always getting the following response from twitter:

{"errors":[{"message":"Could not authenticate you","code":32}]}

I tried this by using my own access token as well as a dynamically created one.

Code for using my own access token:

import org.scribe.builder.ServiceBuilder;
import org.scribe.builder.api.TwitterApi;
import org.scribe.model.OAuthRequest;
import org.scribe.model.Response;
import org.scribe.model.Token;
import org.scribe.model.Verb;
import org.scribe.oauth.OAuthService;

public class TwitterTest {

    public static void main(String[] args) {

        OAuthService service = new ServiceBuilder()
                                    .provider(TwitterApi.SSL.class)
                                    .apiKey("myApiKey")
                                    .apiSecret("myApiSecret")
                                    .build();

        Token accessToken = new Token("myAccessToken", "myAccessTokenSecret");

        OAuthRequest request = new OAuthRequest(Verb.GET, "https://api.twitter.com/1.1/statuses/user_timeline.json");
        service.signRequest(accessToken, request);

        Response response = request.send();
        System.out.println(response.getBody());
    }

}