Cross thread access problem in ResponseCallback in Windows Phone 7

Basically, I'm getting some data from a WebService, and in the ResponseCallback I'm trying to fill an ObservableCollection with the results I got from the response, but I get an UnauthorizedAccessException "Invalid cross-thread access" when I try to do so.

What would be the best way to fill said observable collection when I get the result?

Thanks!

This is the code:

    public ObservableCollection<Person> People { get; set; }

    private void ResponseCallback(IAsyncResult asyncResult)
    {
        HttpWebRequest request = (HttpWebRequest)asyncResult.AsyncState;
        HttpWebResponse response = (HttpWebResponse)request.EndGetResponse(asyncResult);

        string responseString = string.Empty;

        using (Stream content = response.GetResponseStream())
        {
            if (request != null && response != null)
            {
                if (response.StatusCode == HttpStatusCode.OK)
                {
                    XDocument document = XDocument.Load(content);

                    var people = from p in document.Descendants()
                            where p.Name.LocalName == "PersonInfo"
                            select Person.GetPersonFromXElement(p);

                    foreach (Person person in people)
                    {
                        this.People.Add(person); // this line throws the exception
                    }
                }
            }

            content.Close();
        }
    }