JSFiddle - React, Tailwind, and code Playground

HTML

<div class="selectParent">
     <select>
          <option value="1">Option 1</option>
          <option value="2">Option 2</option>           
     </select>  
 </div>

CSS

.selectParent{
    width:80px;
    overflow:hidden;
   
   
}

.selectParent select{
       text-indent: 1px;
text-overflow: '';
	
    width: 100px;
    -webkit-appearance: none;
    -moz-appearance: none;
    appearance: none;
    padding: 2px 2px 2px 2px;
    border: none;
    background: transparent url("http://cdn1.iconfinder.com/data/icons/cc_mono_icon_set/blacks/16x16/br_down.png") no-repeat 60px center;
}