I have no experience at all of ordering chicks mail order BUT I do have a lot of experience with postal services.
You MUST complain to them, you need to get the mailing information from the hatchery and you should also find out how the hatchery marks their boxes (your first box would do fine), armed with that information go to the post office and ask them to find your box.
If they say it's at another post office, get them to get it sent to your local post office where you will pick it up - don't let them send it to your house, it's very unlikely to be your local postmans problem.
When they find your box ('Duh..OK... here it is, we put it under this shelf for safekeeping') open the box in front of them and show them the contents.
Then tell them to make sure that every package sent to your address is treated as if a life depended on it, because in this case it does.
Post Offices can fast track parcels no problem, they sometimes just need reminded that it's not acceptable to leave packages until tomorrow unless they know what is in them. Don't be afraid of feeling that you're asking for better service than the next guy, so few people ask for favors these days that even the post office should be able to treat your packages as priority packages. If the PO worker that you speak to isn't overly helpful just ask to see their manager. I'm not sure how it works in the US but most service type workers would be reprimanded if someone asked to speak to their manager and they refused, and subsequently the manager was contacted and informed of the refusal. If all else fails, go through the Postal Service complaints procedure, you may only get a letter saying 'Sorry, we try hard not to let this happen and we will learn from our mistakes' or you might get some compensation over and above the cost of chicks and delivery.
Don't forget, it's your right to complain about poor service.
I hope your next lot arrive OK