Actually, it does. The datasheet features list includes "Real Time Counter with Separate Oscillator". However, there are some limitations and compromises. The crystal pins are shared, so if the RTC is used, then the system clock must be the internal RC oscillator. This would prevent accurate timing for serial I/O. Also, the time-keeping code needs to be written, but this is nearly trivial, only a dozen lines or so, although an interrupt handler is probably required. Some pains in both hardware and software would have to be taken to achieve extended battery-backup capability.
So quite often an external RTC is not only easier to use, but is a better solution as well. My first thought is that is the way the OP should go.
I did an experimental project using the internal RTC, however there is no backup power, so if the main supply is lost, the time needs to be reset. Adafruit Industries' Ice Tube Clock I believe uses the internal RTC, and achieves some level of battery backup, but not nearly as long as some of the standalone RTCs which can run for years.