The opposite of removal is insertion; there are various ways to insert an element. Since your element is at index 0, prepending it to its original parent element is what you need here.

If you just remove an element without retaining its reference, it’s going to be garbage-collected and you cannot use it anymore. So store a reference to the element; also, store one to its parent, since that’s the target you need to prepend the element to.

const chatElement = document.getElementsByClassName('_1FlWeEtrJKCnvzX-Y50CLP')[0],
  chatParent = chatElement.parentElement;
let isToggled = false;

function doc_keyUp(e) {
  switch (e.code) {
    case KeyH:
      if (isToggled) {
        chatParent.prepend(chatElement);
      }
      else {
        chatElement.remove();
      }

      isToggled = !isToggled;

      break;
    default:
      break;
  }
}

document.addEventListener("keyup", doc_keyUp, false);

Toggling the variable isToggled can be done with isToggled = !isToggled;, but do not redeclare the variable inside the function, or else it will have no relation to your outer isToggled variable.

Note that keyCode is deprecated. You should use code instead.

There are two more concerns:

1. If Cytos depends on the chat existing, then removing the element may cause the app to break. Similarly, removing and reinserting elements may cause unforeseen events to be triggered. Consider using case KeyH: chatElement.toggleAttribute("hidden"); break; instead. See the documentation on toggleAttribute and on the hidden property.
2. The class name _1FlWeEtrJKCnvzX-Y50CLP doesn’t look like a stable class name, but rather like a minified, randomized name. It’s very likely to change and your user script is very likely to break. Familiarize yourself with the DOM API, in particular with document.querySelector, and consider finding a more stable selector.