This answer is more general than DrupalChat module.
Some modules install content types and field types.
My solution is for Drupal 7.x. It's likely similar on
BE SURE to back up the data base before doing these steps.
1) go to .../admin/structure/types. Look for the content type associated with the module. If it's not there, this is not the solution.
2) if there is such content click on manage fields. Remove any field that is also associated with the module. You have to agree to the "this cannot be undone warning".
3) back to admin/structure/types and remove the content type. Again agree to "this cannot be undone warning".
4) go to ../admin/modules and disable the module.
This should work. You may have to work through additional required by modules and any content and fields that those modules added. (Lather, rinse, repeat.)