Please look this example:
select {
width:192px;
padding:2px;
border:none;
background:url(http://imgur.com/MJyZM.png) 0 0 no-repeat;
-webkit-appearance: none;
}
<select>
<option value="abcdefg">abcdefg</option>
<option value="1234567">1234567</option>
<option value="abcdefg">abcdefg</option>
</select>
Not tested on firefox but it seems -webkit-appearance: none;
disables specific behaviours webkit can apply.