I'd say definitely do back first.
It's such a large, complex muscle group it's be best to lift as heavy as you can when training it.
Your bi's will be helping throughout your back work-out and having these fatigued before you even start the back with lower the weight you lift greatly. Especially for such exercises like chin-ups. And chins are a fantastic back exercise.
Bi's aren't large so I wouldn't be worrying so much about how much you COULD be lifting if you did them first. So, I advise, train them after you back, Sir.
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