JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="//netdna.bootstrapcdn.com/twitter-bootstrap/2.3.1/css/bootstrap-combined.min.css">
<script src="//netdna.bootstrapcdn.com/twitter-bootstrap/2.3.1/js/bootstrap.min.js"></script>
<div class='modal'>
    <div class='modal-body'>
        Hello
        <input />
    </div>
    <div class='modal-footer'>
        <button class='btn' data-toggle='modal'>Toggle</button>
    </div>
</div>

CSS

.typeahead.dropdown-menu {

}

.modal-body {
   overflow-y: visible
}
.typeahead {
max-height: 100px !important;
overflow-y: auto  !important;
overflow-x: hidden  !important;
padding-right: 20px  !important;
}

JavaScript

$("input").typeahead({
    source: ["Alpha", "Alphabet", "Alfa", "Armadillo","ksdjflksdjfl","jksdjflsdjl","qi2ueouqwoei","jalhflasdf","pwoipa","ahweurw","qwipoqwieo"]
});