Go onto Chase.com and set up Auto Bill Pay to pay your statement balance. The payment posts automatically to your CC the evening of your payment due date, and to your bank the following day's cycle.

I do this for 2 Chase Visa cards and have had no worries or problems in the past few years that this feature has been available. The nice thing about this is, if during the period between the statement closing date and the payment due date there are returns or other credits to your account, Auto Bill Pay treats these as payments and your actual payment ends up being your closing balance less those amount(s).