CloudWatch log role ARN

I am trying to setup a really basic API with the AWS API Gateway product and it seems I can not find any policies which will suffice for it to log and for that matter even leave the first page of the settings screen. I am stuck here:

URL: http://ift.tt/1PM6Pxn

and my desperations has led to the following permissions being granted to the role:

I've also added the following bespoke policy:

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Action": [
        "logs:CreateLogGroup",
        "logs:CreateLogStream",
        "logs:PutLogEvents"
      ],
      "Resource": "arn:aws:logs:*:*:*"
    }
  ]
}

All to no avail. Whenever I press the save button I get the following:

Any help would be greatly appreciated.