I practice bankruptcy law in Arizona and I have seen this happen with credit unions but never Chase Bank. The bank may have a cross-collateralization clause that pledges your deposit accounts for the debts. I am surprised to hear that this is Chase, though, because I have filed bankruptcy for many clients with Chase accounts and just about everyone owes Chase money and I've never heard of them sucking money from a client's accounts without a garnishment/levy action. Talk to a local attorney, though. The funds may be exempt from garnishment under local law. If this is the case, you'll probably just need to request a hearing (if it was a garnishment) to get the money back. In any event, talk to someone local.
Your unemployment payments are exempt from judgments and if that is all you have in the account, then they should not be allowed to take any of it. That said, they may try to take it if they find out you have the account with them and an unpaid debt. I would urge you to close the account and open with a bank in which you have no outstanding debts. There are still enough banks and credit unions that you should not risk having to get your money back, from a bank that has an unpaid debt.
You should contact a local consumer attorney. California has very good debt collection protection laws. If the bank knew the funds were exempt, they may have violated some of those laws. You can find one through the National Association of Consumer Advocates at www.NACA.net.