Eslint does not recognize private field declaration using nodejs 12

Eslint will not recognize private fields marked with # in class declarations, even though I'm using NodeJS version 12 (which supports them).

I am running NodeJS v12.7.0. I have searched all DuckDuckGo and Goole and I cannot find a plugin or option in eslint which will tell it to accept the private field notation (#). I have emca set to version 10.

class MyClass {
   #foo = 'bar';
   #bar = 'foo';

   constructor(foo, bar) {
      this.#foo = foo;
      this.#bar = bar;
   }
   ...
};

When I run eslint on the above code, I get:

2:3 error Parsing error: Unexpected character '#'

The project I'm working on does not use Babel, and I don't want to have to include it just to make private fields work. Any ideas how to make this work without having to resort to using Babel?

(Nothing against Babel of course, it's just on this particular project I don't want it).