TLC5940 + high current

Mike, help me through this please! My knowledge is limited in this area.

From the datasheet, it looks like the 28-PDIP package has a max dissipation of about 2.4w at 25C.

Now, I if I want all 16 channels at 120mA, and the chip is running at 5V, then I can calculate the dissipation:

16 channels at 5v and 120mA is 165.12 = 9.6 watts

But that doesn't seem right, does it? The chip isn't dissipating 9.6w - the whole circuit is, correct? How do you calculate dissipation of the chip?