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ExchB used to accept Chase cash deposits. Now they accept Bank of America and Wells Fargo deposits only. Since they are an exchange, you still have to buy bitcoins from other sellers; however it is quit easy and fast, and works very well. I am not familiar with Chase quickpay but if your willing to go first and quickpay does not allow charge backs you should have no problem finding sellers to buying bitcoins directly.https://www.exchangebitcoins.com/
Paypal does not allow bitcoin transactions and will close your account if they find out. Since its so easy to charge back a Paypal transaction and bitcoin transactions are not reversible, you should not accept Paypal for bitcoin and will have a difficult time finding someone to sell you bitcoins for Paypal.
N.olmos, thank you for good info!
Yes I have heard that people have used chase Quickpay on bitcoin irc, so I think its safe.