In my opinion, it is a participle that introduces a participial phrase which modifies "you". One could make a case for it modifying "job".
Student or Learner
"You have a difficult job working at the hospital, so try to rest on the train before work."
What is the grammatical role of "working" ?!
***** NOT A TEACHER *****
Like you, I also like modification questions.
I was happy that the teacher tells us that there is "a case" for saying that it is the objective complement of "job."
This sentence sounds somewhat similar: "I got my first job working at a car wash."
I found a great discussion about this sentence while searching the Web. It was asked on September 20, 2011.
Where? Here at usingenglish.com.
Please go to Google and type in these exact words:
"job working at" participle [Archive]
Be sure to use the quotation marks.
I think that you will find the discussion very helpful.
Last edited by TheParser; 15-Nov-2014 at 21:50. Reason: I changed a question to a statement; I forgot two quotation marks.