Are there RTCs with 100Hz output?
The only RTC I know of which worked with hundredths of a second was the long obsolete Intersil ICM7170. The datasheet isn't clear how the 100Hz was achieved. The crystal frequencies which it was designed for are perfect powers of 2: 32.768kHz (i.e \$2^{15}\$), \$2^{20}\$Hz, \$2^{21}\$Hz, \$2^{22}\$Hz, yet the datasheet says it derives a 4000Hz clock from them, from which the 100Hz is derived. 32768Hz is not a multiple of 4000Hz, so this can't be done with a normal divider. They probably used a fractional divider, like supercat describes.  

Anyway, the ICM7170 is obsolete, so we need something different. While there might not be 32kHz RTCs, there are 32.000kHz crystals, and with a 74HC4060 you get an oscillator + divider.  



The 32kHz crystal probably needs the same load capacitor as a 32.768kHz crystal. The 330k\$\Omega\$ resistor limits the drive power to the crystal. This is significantly higher than the 2.2k\$\Omega\$ recommended by NXP; a 32kHz crystal typically has a drive level of less than 1\$\mu\$W. If the oscillator doesn't start decrease the resistor's value somewhat.
Use the :32 output Q5 (pin 5) to get a 1kHz clock which you can feed to your microcontroller interrupt pin.  



You can then use the 1kHz heartbeat interrupt to derive a 10ms software timer.  

edit
Alternatively a microcontroller can be used. This will be slightly more expensive than the 74HC4060, however, and might also consume a bit more power. I've used TI's MSP430F1101 at 32kHz and 3.3V which needed only 4\$\mu\$A though. Run it off the 32kHz crystal and use a timer to output the 100Hz signal. You can even output different frequencies simultaneously, for instance 1000Hz, 100Hz and 1Hz, or select the frequency on a specific output by setting a pair of I/O pins. Or you can select the frequency via the UART.