First Chicago Corp. will buy Gary-Wheaton Corp. for $136.4 million of newly issued First Chicago stock, the banking companies reported. The companies said they signed a letter of intent, with the transaction subject to approval by Gary-Wheaton shareholders and regulatory agencies. The deal is expected to be completed by the end of next June. Gary-Wheaton has assets of $791 million and has subsidiary banks in the Illinois suburbs of Wheaton, Batavia, Fox Valley and Downers Grove. First Chicago has assets of $44 billion.