[c#] Dictionary with list of strings as value

I'd wrap the dictionary in another class:

public class MyListDictionary
{

    private Dictionary<string, List<string>> internalDictionary = new Dictionary<string,List<string>>();

    public void Add(string key, string value)
    {
        if (this.internalDictionary.ContainsKey(key))
        {
            List<string> list = this.internalDictionary[key];
            if (list.Contains(value) == false)
            {
                list.Add(value);
            }
        }
        else
        {
            List<string> list = new List<string>();
            list.Add(value);
            this.internalDictionary.Add(key, list);
        }
    }

}