Yes, it is legal to fill your controlled substance prescription (hydrocodone) out of state.
Assuming your doctor is licensed to practice in his/her state and also has a valid DEA number, you can fill a controlled substance prescription written by them in any state. The doctor must follow the controlled substance prescription rules and regulations of both the state they are licensed in as well as the state in which the prescription is being filled.
Having said that, if you are filling a controlled substance prescription out of state, at a pharmacy that you have never filled at before, that might raise some red flags on the part of the pharmacy. Many pharmacies have their own rules and regulations regarding filling out of state controlled substance prescriptions. Some may not fill it based purely on their policy (to combat drug diversion and prescription forgery).
At the very least, I would expect the pharmacy you drop of your prescription to will call your doctor to verify the legitimacy of the prescription. Therefore, I would recommend dropping off the prescription when you are not in a hurry and when you know your doctor may be available.
It is unfortunate that those with legitimate prescriptions for controlled substances and medical needs are subjected to a discerning eye in situations like these as it can certainly put the patient in an awkward, uncomfortable position...being made to feel as though they are a drug abuser or criminal. Pharmacies are doing their part to combat prescription forgeries and drug diversion as well as protecting themselves from the potential legal liability if they were to fill a fraudulent prescription, many of which happen to be "out of state" written prescriptions.
My best advice is to ensure a smooth prescription filling process is to have your doctor phone the pharmacy you plan on going to so they can make them aware of your situation and why you need a prescription filled that was written out of state. As with many things, communication is key.