JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/jquery-3.2.1.min.js"></script>
<div class="auction ng-scope">
    
    <div class="auction-chat">
        <div class="head">
            <i>Онлайн-чат</i>
        </div>
        <ul class="chat" id="messages-list"></ul>
        <div class="bottom">
            <div class="top-wrap">
                <img src="/avatars/adm.png">
              <div class="action-more ng-isolate-scope more" data-more="">
                 <div class="more-button" data-more-button=""><i class="icon-smile" data-tooltip="Временно недоступно"></i></div>
             </div>
                <div class="input ng-pristine ng-untouched ng-valid ng-isolate-scope" id="chat-input" contenteditable="true" style="width: 665px;"></div>
                <div class="send-button" onclick="chat.sendMsg();"><i class="icon-send"></i></div>
                <ul class="recent-smilies">
               
                </ul>
            </div>
        </div>
    </div>
</div>

CSS

.auction>.auction-chat>.bottom>.top-wrap>.input {
  height: 41px;
  width: 448px;
  margin: 0 20px;
  padding: 12px 10px 10px 40px;
  background: white;
  border: 1px solid #e9ecf3;
  border-radius: 100px;
}

.auction>.auction-chat>.bottom>.top-wrap>*:not(.action-more) {
  float: left;
  height: 40px;
  border-radius: 50%;
}

.fakeinput.dark,
.fakeinput.dark~.placeholder .ph_input,
div[contenteditable=true],
div[contenteditable=true]~.placeholder .ph_input,
input.dark,
input.dark~.placeholder .ph_input,
textarea.dark,
textarea.dark~.placeholder .ph_input {
  padding: 5px 9px 7px;
  border-radius: 1px;
  box-sizing: border-box;
}

.fakeinput,
.fakeinput~.placeholder .ph_input,
div[contenteditable=true],
div[contenteditable=true]~.placeholder .ph_input,
input.big_text,
input.big_text~.placeholder .ph_input,
input.dark,
input.dark~.placeholder .ph_input,
input.search,
input.search~.placeholder .ph_input,
input.text,
input.text~.placeholder .ph_input,
textarea,
textarea~.placeholder .ph_input {
  color: #000;
  padding: 3px 5px;
  margin: 0;
  border: 1px solid #d3d9de;
}

.fakeinput,
div[contenteditable=true],
input.big_text,
input.dark,
input.search,
input.text,
textarea {
  background: #fff;
  -webkit-appearance: none;
  border-radius: 0;
}

.fakeinput,
div[contenteditable=true],
input.big_text,
input.file,
input.search,
input.text,
input[type=button],
input[type=password],
input[type=search],
input[type=submit],
input[type=text],
input[type~=email],
input[type~=password],
input[type~=search],
input[type~=text],
textarea {
  font-size: 13px;
  font-family: -apple-system, BlinkMacSystemFont, Roboto, Open Sans, Helvetica Neue, sans-serif;
  outline: none;
  box-shadow: none;
}

.input {
  position: relative;
  margin: 0 auto 20px auto;
}

div,
li,
p {
  -webkit-tap-highlight-color: transparent;
}

JavaScript

$(document).ready(function() {
          $("div#chat-input").keydown(function(e) {
            console.log(e.keyCode);
            if (e.keyCode == 13) {
              console.log(13);
              $("div#chat-input").focus();
            }
          });

        });