Do I tap my chem-baroness legend for holding before I draw?

Yes — the Chem-Baroness trigger happens when you Hold, which is in the Scoring Step of your Beginning Phase, and your standard turn draw doesn't happen until the Draw Phase afterward.

So the order on your turn is: Beginning Phase (Hold each battlefield you control → Chem-Baroness's "When you or an ally hold" trigger resolves here, and you may exhaust her to play a Gold gear token exhausted) → Channel Phase → Draw Phase (draw 1). The exhaust and Gold token happen before you draw.

Remember it's a may — you only exhaust her if she's Ready, and you're choosing to make the Gold token. (This is also why Heimerdinger can't copy it — it's a triggered exhaust, not a cost — but that doesn't change the timing for Chem-Baroness herself.) Rule 315.2.b; FAQ 10108.