JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.4/themes/ui-lightness/jquery-ui.css">
<select name='input_34' id='input_1_34'  class='small gfield_select' tabindex='1' >
    <option value='29' >Alabama</option>
    <option value='34' >Alaska</option>
    <option value='43' >Arizona</option>
</select>

<select name='input_13' id='input_13' class='small gfield_select'  tabindex="2"> 
    <option value='-1' selected='selected'>Select a base</option> 
    <optgroup class="level-0" label = "Alabama" value='29'>
        <option class="level-1" value="30">Anniston Army Depot</option> 
        <option class="level-1" value="333">Fort Rucker</option> 
        <option class="level-1" value="32">Maxwell-Gunter AFB</option> 
        <option class="level-1" value="33">Redstone Arsenal</option> 
    </optgroup>
    <optgroup class="level-0" value="34" label="Alaska">
        <option class="level-1" value="35">Eielson AFB</option> 
        <option class="level-1" value="36">Elmendorf AFB</option> 
        <option class="level-1" value="37">Fort Greely</option> 
        <option class="level-1" value="38">Fort Richardson</option> 
        <option class="level-1" value="39">Fort Wainwright</option> 
        <option class="level-1" value="40">USCG ISC Kodiak</option> 
        <option class="level-1" value="41">USCG Juneau</option> 
        <option class="level-1" value="42">USCG Ketchikan</option> 
    </optgroup>
    <optgroup class="level-0" value="43" label="Arizona"> 
        <option class="level-1" value="44">USCG whatever</option> 
        <option class="level-1" value="45">USCG whatever</option>
    </optgroup>
</select>

JavaScript

jQuery(document).ready(function() {

    var clone_select = $('#input_13').clone();

    jQuery('#input_1_34').bind('change', function() {
        var selectedValue = jQuery("#input_1_34").val();

        var clone_subset = clone_select
            .find('optgroup[value="' + selectedValue + '"] > option')
            .clone();
        $('#input_13').empty().append(clone_subset);
    });
});