External Memory IC which increments data on a clock pin
You appear to be describing a FIFO chip, and contrary to the other answers, they do exist as COTS products. For example, IDT has a line of chips of that type. Unfortunately, the 1 MB parts (512k &times; 18&nbsp;bits) have prices on the order of $200 in small quantities.

But the rest of your functional description is so vague that I can't be sure. Also, if you have an FPGA in your system anyway, its on-chip block RAM can be configured to do the same thing (assuming that there's enough of it).