How do you set the Content-Type header for an HttpClient request?

The content type is a header of the content, not of the request, which is why this is failing. AddWithoutValidation as suggested by Robert Levy may work, but you can also set the content type when creating the request content itself (note that the code snippet adds application/json in two places-for Accept and Content-Type headers):

HttpClient client = new HttpClient();
client.BaseAddress = new Uri("http://example.com/");
client.DefaultRequestHeaders
      .Accept
      .Add(new MediaTypeWithQualityHeaderValue("application/json"));//ACCEPT header

HttpRequestMessage request = new HttpRequestMessage(HttpMethod.Post, "relativeAddress");
request.Content = new StringContent("{\"name\":\"John Doe\",\"age\":33}",
                                    Encoding.UTF8, 
                                    "application/json");//CONTENT-TYPE header

client.SendAsync(request)
      .ContinueWith(responseTask =>
      {
          Console.WriteLine("Response: {0}", responseTask.Result);
      });

For those who didn't see Johns comment to carlos solution ...

req.Content.Headers.ContentType = new MediaTypeHeaderValue("application/octet-stream");