You'll need to either insert BR tag appropriately in the resulting string, or use for example a PRE tag so that the formatting of the stringify is retained:

var data = { a: 1, b: 2 };

var Hello = React.createClass({
    render: function() {
        return <div><pre>{JSON.stringify(data, null, 2) }</pre></div>;
    }
});

React.render(<Hello />, document.getElementById('container'));

Working example.

Update

class PrettyPrintJson extends React.Component {
    render() {
         // data could be a prop for example
         // const { data } = this.props;
         return (<div><pre>{JSON.stringify(data, null, 2) }</pre></div>);
    }
}

ReactDOM.render(<PrettyPrintJson/>, document.getElementById('container'));

Stateless Functional component, React .14 or higher

const PrettyPrintJson = ({data}) => {
    // (destructured) data could be a prop for example
    return (<div><pre>{ JSON.stringify(data, null, 2) }</pre></div>);
}

Or, ...

const PrettyPrintJson = ({data}) => (<div><pre>{ 
    JSON.stringify(data, null, 2) }</pre></div>);

Working example

Memo / 16.6+

(You might even want to use a memo, 16.6+)

const PrettyPrintJson = React.memo(({data}) => (<div><pre>{
    JSON.stringify(data, null, 2) }</pre></div>));