Do I really need Babel or other transpilers to use ES6 in React?
I was looking at the chart https://kangax.github.io/compat-table/es6/
Seems like my current browser Chrome (latest stable version) supports almost all the ES6 features...
If I can use ES6 without Babel, how I should do it?
Without babel you get the compatibility of the chart you linked to. But keep in mind if you want to use JSX you'll want to use babel to transpile that.