you should power the chip from arduino (either 3.3v or 5v depending on your resistor for IREF).
what i meant to say in my post is that i have an external power supply for the LED's (not the TLC5940).... and a common ground between all three (the ground of the power supply is connected to ground on arduino and the TLC5940).
also: do you have the 1uf capicator shown in the schematic in your circuit? this will reduce noise from the circuit; maybe the capicitance or magnetic field of your body is affecting the circuit...????