That 10c microcontroller has 15 32 bit registers, allowing you to make up to a 480 bit counter. That ought to be enough until long after the heat death of the universe.

It also has 2k (16384 bits) of SRAM, allowing even larger counters.

It runs off 2.8V - 5.5V DC, so supplying power is pretty trivial. Doesn't need a crystal, though of course adding one will improve the timing accuracy.