Can a Brand Name be used withought infringing on the Trademark?

Trademarks are NOT word monopolies. Infringement only occurs when someone uses another's trademark IN COMMERCE -- that is, when offering goods or services for sale. Your intended use of "Chase" is clearly not for commercial purposes and so trademark law is not implicated AT ALL.

Make and distribute your flyer and have a good time at the party.

Yes, there's a loophole in trademark law. It's called "nominative fair use," and it means you can MENTION someone else's trademark in decribing something, like describing yourself as an employee of the bank called Chase, as long as you don't USE the mark to confuse anyone about whether your party is sponsored by the trademark owner. So your flyer can't say "Chase's employee's party."

You're not a competitor of Chase, so you probably wouldn't be accused of infringement anyway, but there's more that you can do. Putting the R symbol to indicate that it's a registered mark is part of what you have to - the other part is to include a disclaimer saying that your party is not sponsored by Chase, and that the chase TM is a registered mark of [owner].

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.