callback async loop

myStream.read(function handleChunk(chunk) {
  if (!chunk) {
    processDone();
    return;
  }
  processChunk(chunk);
  myStream.read(handleChunk);
});

promise async loop

myStream.read().then(function handleChunk(chunk) {
  if (!chunk) {
    return;
  }
  processChunk(chunk);
  return myStream.read().then(handleChunk);
}).then(processDone);

The following code (more similar to your callback code) would also not have this problem:

myStream.read().then(function handleChunk(chunk) {
  if (!chunk) {
    processDone();
    return;
  }
  processChunk(chunk);
  myStream.read().then(handleChunk);
});