Variants of this question have been discussed on SO a bunch of times already, and unfortunately you won't find a perfect answer, as there isn't one.
Essentially, you want to ship authentication credentials in your app, i.e. you bundle a secret into it. This means that no matter what you do, there's a possibility that an attacker retrieves it via reverse engineering. Even if you encrypt it with a hard algorithm that is technically secure enough, at some point your app decrypts it and since the app might be in the hands of an attacker, they will be able to sniff the secret.
This means in the end you can only try to make it hard for them by basically obfuscating the way in which you handle the secret ("make sniffing complicated"). Bundling an encrypted file that gets decrypted and then packed into the keychain seems not like a bad idea to me for a start, but keep in mind that for somebody looking at your app, especially on a jailbroken iPhone, this vanishing file can be a good first hint. Also, deleting it doesn't really help, as one re-install easily restores it.
Another idea could be to use On-Demand Resources to distribute your secret, this might also make it easier to replace it with an updated version in case your secret gets compromised. I am not that familiar with on-demand resources myself, though, so I can't tell you how suited they would be for actually revoking things.
This all assumes that you have no way of implementing an authentication mechanism based on user input. That way an attacker could only steal their own password (assuming they don't steal someone else's iPhone...) and not a vital part of your entire app (which could potentially affect all users).
Other SO answers from my bookmarks that might help you are these:
Okay, after re-reading your last comment under the question again, here's a concrete suggestion. I don't know why you need this second password/token at all if you're already having user authentication (you talk about them logging in), but here you go:
- You don't bundle a token/pass together with the app at all. When first running your app, user's have to log in anyways (if I got you right), so your server can be involved and this is where you start.
- During this login, the server generates a token/password and will send this to the user (depending on your exact implementation/custom protocol this might be done in a second request/response done by the app that uses the same user credentials or you put it into the headers of the response to the very first request sent by the app). Note that you don't need to encrypt this as long as you use https, as this already encrypts this data. So the channel by which your token arrives within your app is secure.
- The app then saves this token/pass in the keychain immediately. This is as good encrypted as it gets on a mobile device. Do not save the token in anything else, even temporarily. The pass only ever exists in plain when it's in memory (you can't avoid that).
- You use that token for whatever you need it (I am actually wondering why you need it if you're already using https and a user login system at all).
All in all this sounds like a pretty standard pseudo-OAuth-like token approach, if you're just wanting to use the token to avoid always relying on the user credentials (username and password) in each request. Technically you could also just save username and password in the keychain and always get those for each request. Usually these tokens have a limited time-to-live after which they become invalid anyways and the app has to rely on username and password again to get a new one anyways.
The potential downside of a token is if it's static and not user-bound or if it doesn't have this time-to-live limit. You would have to generate this in a clever way on the server and obviously note which user uses which token. That way you can pinpoint security breaches and react accordingly (instead of suddenly shutting down the server for all users by invalidating your one and only token). Again, I don't see why you need this, though.
Regarding a man-in-the-middle attack: A token, be it app-bundled (which is a risk in itself) or server generated, doesn't in itself protect against that. I have no idea what your boss would aim for here, but perhaps I'm missing some information. In general, https already protects you from this (well, usually only the server is authenticated, but if you already have a username and password system, you should be fine for the client side, too). It's actually a big point of it in general. To me this sounds more and more like something in your original problem is simply a misunderstanding of the existing infrastructure and/or a "boss-induced" problem... :)