Is a quiver of arrows a single item or 21 separate items under RAW? I'm making a zen archer monk and am wondering if the "Vow of Poverty" is unobtainable with that build.
The price includes miscellaneous gear that goes with the weapon, such as a scabbard or quiver.
so I think we can conclude that the quiver counts as part of the bow. As for the arrows, if a pair of shoes can count as one item, 20 arrows should also count as one item.
There's a separate problem, which is that your bow is an item and your arrows are also an item. Vow of Poverty only gives you one flex item -- "a simple set of clothing, a pair of sandals or shoes, a bowl, a sack, a blanket, and any one other item" -- so it won't let you carry both.
You could work around this problem by using a bow of endless ammunition but that's awfully expensive and probably not worth it.
A better plan might be to politely ask your DM to houserule that you can carry arrows for your bow.
Vow of Poverty accepts that an array of several discreet objects can be one possession.
Look no further than the list of possessions enumerated in the vow, itself: the monk is permitted a set of clothes and a pair of shoes. A sash, tunic, two sandles, chestbindings, and holy underwear are all only only two possessions, even though those posessions are comprised of six objects in total.
In this way, a quiver of arrows is, too, a single possession.
To answer your implicit question, it being, "How can my poverty-sworn monk employ a bow with arrows?"—
A clutch of arrows is expendable, much as a bowl of rice. For your consideration: The act of possession is the act of using, but with an arrow, the act of using is the act of de-posessing. That which is ephemeral, then, is only truely owned when it has already been given up! Meditate on this koan, and write it down in your analects, or, whatever. The point is, arrows are categorically more similar to the upkeep described in the next clause:
The monk can never keep more money or wealth on his person than he needs to feed bathe, and shelter himself for 1 week in modest accommodations.
And while we're on that subject, "Wealth" is equatable to "anything of commodified value." Through barter, arrows can be your means of exchange. If you put ranks in Craft: Fletching, it's not even wierd that making arrows would be your principal means of earning sustainance (and since you're a badass who would otherwise stand to earn a lot more money by simply accepting your due on the Wealth-By-Level table, making arrows for your daily bread is the very definition of humility). So, if you just get in the practice of trading them for a sandwich every now and then, you can use them in the meantime to shoot people. Maybe even just shoot at animals and eat them.
Failing any of that:
He cannot borrow or carry wealth or items worth more than 50 gp that belong to others.
Exceptio probat regulam. Feel free to carry around up to a thousand of somebody else's arrows. Hell, you don't even need to have friends to make this work; every arrow you obtain, swear to somebody else. Swear that you're going to employ that arrow in its owner's name, or that you're merely holding it and they can reclaim it whenever they find it convenient to receive it from you. Or, swear that your arrows all belong to your various enemies, and set forth to return them... At high velocity. Either is within the letter of the RAW.
I would love to be your DM on this! In fact I would use this as the starting point in fracturing your monastery as the monks are faced with an unanswerable question.* What a great plot device.
You asked about RAW though. The rule book doesn't specifically address this exact scenario in handling items that are a bundle yet also singular. I would rule each arrow an item.
*If you don't understand why that question could lead to a heated debate answer me this. Is it a single bale of straw or a million pieces wrapped together?