Depending on which account they are (With Chase I'm assuming either a Chase Savings or a Money Market Savings) you should proactively close them. You may be charged a fee if they stay open and at $0, depending on the account type and how it is linked internally.
I keep a savings open because it is free for me and gives me a place to temporarily store funds until they move into an investment account. I do not find value in keeping any funds in a savings - I do keep some money in my brokerage's MMA, but that is only for emergencies. (Yes, I understand that in the MMA it is at risk).
Definitely close them. Even if they're not charging fees now, they might in the future (a lot of banks have recently started charging fees, or changing the minimum requirements to avoid fees).
If you don't use the account, you might not notice the fees, but they'll still try to get your money.
On a related note - If a bank ever tries to charge you a one-time fee, talk to the manager at your local branch and ask to have the fee removed. If you've been with them for awhile, there's a good chance they will if you ask nicely.
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