>   I currently don't have any capacitors across the supply line.  (I am using a lab 
>   quality power supply for testing, but it certainly doesn't mean that the leads in
>   aren't picking up noise.... a good point to remember
>   
Regardless of the quality of the power supply you need reasonable sized 
(100nf or more) low ESR (generally ceramic caps are used) caps across 
the power supply as close as possible to each pair of power supply pins.

Noise pickup isn't the reason and neither is noise from the power 
supply. The reason is that logic chips tend to draw short high current 
spikes as they switch. Such current spikes do not travel well down 
cables or PCB tracks due to the parasitic inductance so they must be 
supplied by low ESR caps close to the chip.

It is also advisable to have a bulk capacitor (a few microfarads of 
electrolytic or tantalum) accross the power supply somewhere on the 
board but with a good power supply that isn't so important.
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