How to use wp_category_checklist()?

Here is the answer I ended up with:

$select_cats = wp_dropdown_categories( array( 'echo' => 0 ) );
$select_cats = str_replace( "name="cat" id=", "name="cat[]" multiple="multiple" id=", $select_cats );
echo $select_cats;

It displays a list of my categories that can be multi-selected as per my question. It’s a hack of wp_dropdown_categories, but it works.