Consumer Checking Account Equity Act of 1979 - Amends the Federal Reserve Act and the Federal Deposit Insurance Act to authorize member banks in the Federal Reserve System and federally insured nonmember banks to make automatic funds transfers from a savings deposit to a demand deposit pursuant to the written authorization of the depositor to make such transfers in connection with checks or drafts drawn upon the bank. Authorizes federally insured banks and savings and loan associations, State banks and savings and loan associations, savings banks, and mutual savings banks to offer interest-bearing deposits or accounts upon which the depositor may make withdrawals by negotiable instrument for the purpose of making transfers to third parties (NOW accounts). Stipulates that such deposits or accounts may only be held by individuals or nonprofit organizations. Amends the Home Owners' Loan Act of 1933 to permit Federal savings and loan associations and Federal mutual savings banks to establish remote service units pursuant to regulations of the Federal Home Loan Bank Board. Authorizes such associations to extend loans directly related to negotiable order of withdrawal accounts. Amends the Federal Home Loan Bank Act to require any institution which has subscribed for the stock of a Federal Home Loan Bank to maintain reserves against its negotiable order of withdrawal accounts pursuant to regulations prescribed by the Board after consultation with the Board of Governors of the Federal Reserve System. Prescribes the required form of such balances. Amends the Federal Credit Union Act to permit insured credit unions to offer share draft deposits to individuals and nonprofit organizations in accordance with regulations prescribed by the National Credit Union Administration Board. Requires each Federal credit union to maintain reserves against such deposits in amounts and forms prescribed by the Board after consultation with the Board of Governors of the Federal Reserve System.