You do not need to eject.
Create-React-App supports css modules right out of the box as of version 2, which is now stable.
Upgrade to v2 (react-scripts@latest) by running yarn upgrade react-scripts@latest.
You just have to create a file with the extension .module.css
For example:
.myStyle {
color: #fff
}
Then you can use it like so:
import React from 'react'
import styles from 'mycssmodule.module.css'
export default () => <div className={styles.myStyle}>We are styled!</div>
To read more - https://facebook.github.io/create-react-app/docs/adding-a-css-modules-stylesheet