<div id="mount-point"></div>
* {
  box-sizing: border-box;
}

body {
  padding: 20px;
  background: #2c3e50;
}

.filter-list {
  margin: auto;
  width: 300px;
  background: #3498db;
  border-radius: 5px;
  border: 1px solid darken(#3498db, 20%);
  input {
    width: 100%;
    display: block;
    padding: 10px;
    border-radius: 5px 5px 0px 0px;
    border: 0;
    font-size: 24px;
    &:focus {
      outline: none;
    }
  }
  ul {
    margin: 0;
    padding: 0;
    li {
      list-style-type: none;
      margin: 0;
      color: white;
      padding: 10px 20px;
      border-top: 1px solid darken(#3498db, 20%);
      &:hover {
        background: #2980b9;
      }
    }
  }
}
View Compiled
/** @jsx React.DOM */

var List = React.createClass({
  render: function(){
    return (
      <ul>
      {
        this.props.items.map(function(item) {
          return <li key={item}>{item}</li>
        })
       }
      </ul>
    )  
  }
});

var FilteredList = React.createClass({
  filterList: function(event){
    var updatedList = this.state.initialItems;
    updatedList = updatedList.filter(function(item){
      return item.toLowerCase().search(event.target.value.toLowerCase()) !== -1;
    });
    this.setState({items: updatedList});
  },
  getInitialState: function(){
     return {
       initialItems: [
         "Apples",
         "Broccoli",
         "Chicken",
         "Duck",
         "Eggs",
         "Fish",
         "Granola",
         "Hash Browns"
       ],
       items: []
     }
  },
  componentWillMount: function(){
    this.setState({items: this.state.initialItems})
  },
  render: function(){
    return (
      <div className="filter-list">
        <input type="text" placeholder="Search" onChange={this.filterList}/>
      <List items={this.state.items}/>
      </div>
    );
  }
});

React.renderComponent(<FilteredList/>, document.getElementById('mount-point'));

External CSS

This Pen doesn't use any external CSS resources.

External JavaScript

  1. https://codepen.io/chriscoyier/pen/yIgqi.js
  2. https://cdnjs.cloudflare.com/ajax/libs/react/0.11.1/react.js
  3. https://cdnjs.cloudflare.com/ajax/libs/react/0.11.0/JSXTransformer.js