Rock, Paper, Scissors -> Is there a simpler way to do this?

rockpaperscissors.js

var userChoice = prompt("Do you choose rock, paper or scissors?");
var computerChoice = Math.random();
if (computerChoice < 0.34) {
  computerChoice = "rock";
} else if(computerChoice <= 0.67) {
	computerChoice = "paper";
} else {
	computerChoice = "scissors";
}

var compare = function(choice1, choice2) {
    if (choice1 === choice2) {
        return "The result is a tie!";
    }
    
    if (choice1 === "rock") {
        if (choice2 === "scissors") {
            return "rock wins";
        } else {
            return "paper wins";
        }
    }
    
    if (choice1 === "paper") {
        if (choice2 === "rock") {
            return "paper wins";
        } else {
            return "scissors wins";
        }
    }
    
    if (choice1 === "scissors") {
        if (choice2 === "paper") {
            return "scissors wins";
        } else {
            return "rock wins";
        }
    }

    if (choice1 != "rock" || choice1 != "paper" || choice1 != "scissors") {
	return choice1.toUppercase() + " is not a valid choice!";
};

compare(userChoice, computerChoice);

You could make the choices an array and then make the computer pick a random choice - save doing the if/else statement and then assigning the choice (not tested yet):

var choices = ['rock', 'paper', 'scissors'];
var computerChoice = choices[Math.floor(Math.random() * myArray.length)];

Because you're only choosing the winning result, you don't really need to nest your checks, the order doesn't matter. I don't know of any nice native Javascript array comparison methods but you could use #some a bit like this...

var rockChosen = bothChoicesAsArray.some(function(c) { return c == 'rock' });
var scissorsChosen = bothChoicesAsArray.some(function(c) { return c == 'rock' });

if( rockChosen && scissorsChosen) then do something

You could probably squeeze it down a little more by pulling out the check into a separate re-useable function.