JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js"></script>
<div class="fancyContainer">
  <ul class="chatBox">
    <li class="him">Hello... This is a chatbox.</li>      
    <li class="me">Well well. I guess this is a chatbox.</li>
    <li class="me">I'll have to talk about this some other time.</li>
    <li class="me">No wait. I might change my mind</li>
    <li class="him">Nonesense good sir! We'll have this talk right now and here.</li>
    <li class="him">I Like...</li>
    <li class="him">popsicles.</li>
    <li class="me">I can't believe you've done this to me!</li>
  </ul>
</div>

CSS

.fancyContainer{
  border: 1px solid #555;
  position:relative;
  width:300px;
  padding:5px;
  overflow:hidden;
}
.chatBox {
  width: 300px;
  list-style: none;
  margin: 0 0 0 -40px;
  position:0;
}

.chatBox li {
  margin: 5px 0 5px 0;
  padding: 3px 5px 3px 5px;
}

/*Set up initial chat element for .me*/
.chatBox .me {
  min-height: 20px;
  float:right;
  clear: both;
  background-color: #34a1ef;
  border-radius: 10px 2px 2px 10px;
}

/*Set up initial chat element for .him*/
.chatBox .him {
  min-height: 20px;
  float:left;
  clear: both;
  background-color: #ddd;
  border-radius: 2px 10px 10px 2px;
}
/*Set up grouped radius*/
.him + .me {
  border-top-right-radius:10px;
}
.me + .him {
  border-top-left-radius:10px;
}
.me + .me {
  border-bottom-right-radius:2px;
}
.him + .him {
  border-bottom-left-radius:2px;
}


/*Set up First and Last radius for .me*/
.chatBox > .me:first-child {
  border-top-right-radius:10px;
}
.chatBox > .me:last-child{
  border-bottom-right-radius:10px;
}

/*Set up First and Last radius for .him*/
.chatBox > .him:first-child{
  border-top-left-radius:10px;
}
.chatBox > .him:last-child{
  border-bottom-left-radius:10px;
}

JavaScript

/*$('.chatContainer li:first').css('border-top-right-radius', '10px');
$('.chatContainer li:last').css('border-bottom-right-radius', '10px');*/