Can I prevent that Chrome (v45) pauses on promise rejections?

Chrome only does this if you have "pause on uncaught exception" turned on in the "Sources" tab.

If you untick it it will not pause on errors.

A promise rejection is conceptually an error. It is the correct way to mentally model it, otherwise the following are silent errors:

Promise.resolve().then(function(){
    JSON.prase("{}"); // unhandled rejection, TypeError, typo
    foooooo = 15; // unhandled ReferenceError, undefined
});

And so on.

If you want to explicitly suppress a rejection, which is akin to a synchronous "catch all" you'd do the same thing you do in synchronous code:

try {
   doSomething();
} catch(e){
    // explicitly ignore all errors.
}

With promises:

doSomething().catch(function(){}); // explicitly don't report rejection

It is interesting to notice that rejecting a promise syncronously throws an Error while asynchronously doesn't. Consider this example:

var willIGetNewPhone = ()=>new Promise(
  (resolve, reject)=>{
    setTimeout(()=>{
      var reason = new Error('mom is not happy');
      reject(reason);
    }, 1000);
  }
);

willIGetNewPhone()
  .catch(error=>{
    console.log(error.message);
  });

This code doesn't throw exception. But if setTimeout part is removed the exception is thrown.