HSA accounts come with various rules intended to ensure that the pre-tax money you have opted to put into your HSA account is indeed used for appropriate purposes. Most employers don't handle these accounts in-house but contract with a company or bank who offers to take care of the details and the necessary accounting: the money is simply sent to the bank, and it is the bank that is responsible for ensuring that the money is indeed used appropriately. Now, if you say that you want Wells Fargo (to pick another bank as an example) to handle your HSA account, the
employer will likely need to have a
contract with Wells Fargo too, and Wells Fargo will charge you fees to handle
the account also. Whether you will be any happier with Wells Fargo's fees for
a one-off HSA account versus Chase's fees where a (smaller)
bulk rate might be charged is something that you should find out before
approaching your employer with a request to have Wells Fargo handle your
HSA account.