Setting up multi-select with react-select

I'm probably just overlooking something, but I am unable to figure out why I can't seem to configure a multi-select with react-select.

Here's a working example of what I'm seeing.

Notice that only one item can be selected on the multiselect, and then the dropdown no longer loads until the current item is cleared. Also, when the item is cleared, and you can see all the options, it looks like the highlight on mouseover no longer works.

Code:

import React from "react";
import { render } from "react-dom";
import Select from "react-select";
import "react-select/dist/react-select.css";

class App extends React.Component {
  constructor() {
    super();
    this.state = {
      multiValue: null,
      filterOptions: [
        { name: "foo", label: "Foo" },
        { name: "bar", label: "Bar" },
        { name: "bat", label: "Bat" }
      ]
    };

    this.handleMultiChange = this.handleMultiChange.bind(this);
  }

  handleMultiChange(option) {
    this.setState(state => {
      return {
        multiValue: option
      };
    });
    console.log(option);
  }

  render() {
    return (
      <div>
        <label>Multi (not working)</label>
        <Select
          name="filters"
          placeholder="Filters"
          value={this.state.multiValue}
          options={this.state.filterOptions}
          onChange={this.handleMultiChange}
          multi
        />
      </div>
    );
  }
}

render(<App />, document.getElementById("root"));