From their webpage:
Here’s their 990.
Thank you, I sit corrected. Imma beat up that little mouthy Cub Scout who miseducated me. 
I would argue that it’s not trivial at all. Oh, sure, anyone *can *do it, but will they do it right? Doing it wrong is easy. Very few people have the expertise to do it correctly.
Doing it wrong may or may not bother the BSA at all - you’ll undoubtedly have a legal entity of one type or another and BSA is pretty flexible about the kinds of entities that are eligible to be COs.
Well I was going to correct you that schools (public schools anyway) can’t charter scout packs/troops, then I saw this post:
Is that a public elementary school?
They can’t do that - an endorsement of the scouts is an endorsement of a religious organization, and therefore a violation of the Establishment Clause if an arm of the government does it. Our local Cub Scout pack holds its meetings at the school, but is sponsored by a small nearby church.
So I hope you’re referring to a private elementary school, else they could have a lawsuit coming their way.
First of all, what makes you say that the BSA is a religious organization? One could argue, perhaps, that a troop sponsored by a church is, but that’s not what you’re talking about.
Second, the BSA is itself endorsed by the US Congress, so even if there were an objection to be made there, it’s one that’s apparently ignored by Congress and the courts.
Eh? No. Schools are free to acknowledge religious groups as long as they aren’t getting special favors. Otherwise there would be no Fellowship of Christian Athletes, among much else.
There are many public schools in many states that sponsor scout units. It would only be a first amendment violation if you were required to join. And then it would be for freedom of assembly, not freedom of religion
It would also be a first amendment violation if the school was providing financial support.
I suspect in many places, the public school district has nothing to do with Boy Scouts (including providing meeting space ) for reasons unrelated to the first amendment , and in many others, the actual chartering organization is a parent-teacher association of some kind although parents wouldn’t necessarily make that distinction Chartered Organizations
You’re going to have a hard time arguing that the scouts are a religious organization, and once you do that, that public entities cannot support them.
When I was a Boy Scout, the chartering organization for my first troop (in Tennessee) was the local public middle school. The CO for my second troop (in Illinois) was actually the U.S. Army post where we lived.
Today, the town I live in (in Connecticut) actually has three Boy Scout troops, all chartered by different churches of different denominations. My family is (nominally) Catholic, but this had no bearing on which troop my son picked. He picked the troop that seemed to have the best program (and the one that his friends went to). The church that sponsors my son’s troop is some brand of Protestant church, but that’s about all I can tell you about it. The church certainly does not impose its beliefs on Scouts who are in the troop.
Looks like several folks have already addressed it, but yes, it’s the local public school. Which is not at all uncommon (at least around here). The next-closest elementary school to us also sponsors a cub pack.