ATTiny85 - Welcome to Las Vegas!

The TLC5940 does need a total of four connections to the processor which may make it a little difficult to use with a t85. I know the TLC5940 works well with a t84.

If you don't need PWM (or are willing to mimic it using software), the TLC5916 is a nice inexpensive alternative to the TLC5940 that needs the usual three connections to the processor.