It's really hard to say anything just from your description.

I guess the some basic questions would be
Where does this noise comes? what is the noise voltage profile, low frequency or high frequency? Is it from the PCB, assuming you are using PCB to test the ADC, or on chip?

How does it couples to the supply?

One more thing, is it really noise? Check the way you measure it to make sure what it is.

Hope this helps.