Pick a random value from an enum?

If I have an enum like this:

public enum Letter {
    A,
    B,
    C,
    //...
}

What is the best way to pick one randomly? It doesn’t need to be production quality bulletproof, but a fairly even distribution would be nice.

I could do something like this

private Letter randomLetter() {
    int pick = new Random().nextInt(Letter.values().length);
    return Letter.values()[pick];
}

But is there a better way? I feel like this is something that’s been solved before.