enable cors in .htaccess

As in this answer Custom HTTP Header for a specific file you can use <File> to enable CORS for a single file with this code:

<Files "index.php">
  Header set Access-Control-Allow-Origin "*"
  Header set Access-Control-Allow-Methods: "GET,POST,OPTIONS,DELETE,PUT"
</Files>

Instead of "*" you can put specific origin (protocol + domain+ optional port).

This is what worked for me:

Header add Access-Control-Allow-Origin "*"
Header add Access-Control-Allow-Headers "origin, x-requested-with, content-type"
Header add Access-Control-Allow-Methods "PUT, GET, POST, DELETE, OPTIONS"

Should't the .htaccess use add instead of set?

Header add Access-Control-Allow-Origin "*"
Header add Access-Control-Allow-Methods: "GET,POST,OPTIONS,DELETE,PUT"

Since I had everything being forwarded to index.php anyway I thought I would try setting the headers in PHP instead of the .htaccess file and it worked! YAY! Here's what I added to index.php for anyone else having this problem.

// Allow from any origin
if (isset($_SERVER['HTTP_ORIGIN'])) {
    // should do a check here to match $_SERVER['HTTP_ORIGIN'] to a
    // whitelist of safe domains
    header("Access-Control-Allow-Origin: {$_SERVER['HTTP_ORIGIN']}");
    header('Access-Control-Allow-Credentials: true');
    header('Access-Control-Max-Age: 86400');    // cache for 1 day
}
// Access-Control headers are received during OPTIONS requests
if ($_SERVER['REQUEST_METHOD'] == 'OPTIONS') {

    if (isset($_SERVER['HTTP_ACCESS_CONTROL_REQUEST_METHOD']))
        header("Access-Control-Allow-Methods: GET, POST, PUT, DELETE, OPTIONS");         

    if (isset($_SERVER['HTTP_ACCESS_CONTROL_REQUEST_HEADERS']))
        header("Access-Control-Allow-Headers: {$_SERVER['HTTP_ACCESS_CONTROL_REQUEST_HEADERS']}");

}

credit goes to slashingweapon for his answer on this question

Because I'm using Slim I added this route so that OPTIONS requests get a HTTP 200 response

// return HTTP 200 for HTTP OPTIONS requests
$app->map('/:x+', function($x) {
    http_response_code(200);
})->via('OPTIONS');