Hello @Anonymous, welcome to My Fico Forums!
I went through several new Chase apps in the past 18 months. After 9/11 and the follow-on USA Patriot Act of 2001, lenders are required to verify identity carefully and some like Chase take it very seriously. I use a P.O. Box for my important mail, yet even though they knew this through another card I already had with them, they withheld my application for new cards if I used that address instead of my street address. It was withheld from their fraud prevention department, I believe. So when your app went to 7-10 days, you likely would have been denied conditional on providing the address information. However, once you supplied it, it restarted the process (ergo, the 30-day message). So hopefully you're back on track!
Good luck with the card and keep us informed about the outcome! The forum has a section for "Credit Card Approvals" and I hope to see you posted there soon! 
Sounds to me like you are still in consideration so that is always a plus. I would be most concerned when it switches to denial.
For now enjoy the wait as this is a Chase card so it is worth it. Usually the length stated is dependent on where in the process your application is so 30 days is just the generic reason that they use to say anything not processed.
@Anonymous wrote:Thanks everyone for the nice words and explanation! It puts me a little at ease, but fingers crossed... I'll keep you updated!
And yes @Aim_High, I live at a school dorm and use my school PO box. It makes a lot of sense, then!
Ouch. In that case you are going to have a hard time getting any card. Those university PO Box units are reused often. The better universities will cycle once per entrance but the worse ones will cycle every year as you get shuffled from dorm to dorm. Great for the university horrible for anyone sending anything to you.
@Anonymous wrote:Thanks everyone for the nice words and explanation! It puts me a little at ease, but fingers crossed... I'll keep you updated!
And yes @Aim_High, I live at a school dorm and use my school PO box. It makes a lot of sense, then!
Ah ha! There you go. That's probably all it was. It may be a little bit of a hassle, but if you still have a physical street address somewhere that would be the best address to put on future credit card apps. Once it gets connected to your credit report, it just expedites the approval process. Then, once the card is approved and mailed, you can go online and change the address of record in your profile. It adds a step but it may simplify things. Some companies allow you to keep both a "physical" address of record and also a "mailing" address of record, but sometimes you can only have one or the other. It's usually simple to change. If you can't find it on the website, just call the customer service number on your card and they'll be glad to help.
