Final answer:
True, modern CPU chips do contain a memory cache directly on the chip, enabling faster data access and improved performance.
Step-by-step explanation:
The statement that modern CPU chips contain a memory cache right on the chip is True. Contemporary CPUs are equipped with multiple levels of cache integrated directly onto the processor die. This allows the CPU to access frequently used data much faster than if it had to retrieve it from the main system memory (RAM). The cache is a small amount of very fast memory and it's a key feature that enables processors, like the mentioned Pentium chips, to execute a high number of instructions per second. The microchip technology has evolved to include complex integrated circuits that make it possible for today's computers to be much smaller and more powerful than those from a few decades ago, which used to fill entire rooms.