JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/2.3.1/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/2.3.1/css/bootstrap.min.css">
<link rel="stylesheet" href="https://raw.github.com/jdewit/bootstrap-timepicker/v0.2.1/css/bootstrap-timepicker.min.css">
<script src="https://raw.github.com/jdewit/bootstrap-timepicker/master/js/bootstrap-timepicker.js"></script>
<link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/2.3.1/css/bootstrap-responsive.min.css">
<div class="input-append bootstrap-timepicker">
<input id="timepicker1" class="input-small" type="text">
<span class="add-on">
<i class="icon-time"></i>
</span>
</div>

CSS

.bootstrap-timepicker{
    position: relative;
}
.bootstrap-timepicker .open{
    display:block;
}

JavaScript

$('#timepicker1').timepicker();