[c#] Multi-key dictionary in c#?

I frequently use this because it's short and provides the syntactic sugar I need...

public class MultiKeyDictionary<T1, T2, T3> : Dictionary<T1, Dictionary<T2, T3>>
{
    new public Dictionary<T2, T3> this[T1 key]
    {
        get
        {
            if (!ContainsKey(key))
                Add(key, new Dictionary<T2, T3>());

            Dictionary<T2, T3> returnObj;
            TryGetValue(key, out returnObj);

            return returnObj;
        }
    }
}

To use it:

dict[cat][fish] = 9000;

where the "Cat" key doesn't have to exist either.