Measuring micro volts DC signal

I have a ~ 10 milli-volts DC signal from an on chip resistor, and I want to be able to read a 7 micro -volts change in signal from it. 
Currently I am using a benchtop highly accurate current source, to supply 1 milli amps to the 10 Ohm resistor, and in a four -wire measurement, I measure the voltage across the biased resistor with an Agilent DMM. 

The noise of my current benchtop set up, where i am using triax connectors (with triax to bnc adapters, and other kelvin connectors), to my device and measuring voltage from chip using open wires and cables to a DMM, always reaches ~ 10 - 100 micro-Volts. I can sometimes get it down to 10 micro-Volts pk-pk  (with help of faraday cage and proper grounding) but not better than that.

If I need to measure a 7 micro-V change in signal with this noise, what is my best bet at the moment? 
Should I move everything on board, and read the voltage with an on board ADC+microcontroller?   Will that reduce the noise in the milli-volts signal? Has anyone here ever measured uV signal change from a mV DC signal? 

My other option exciting the resistor with an AC current, and moving my voltage signal to a higher frequency where there is less noise. 
What do u guys recommend?