I have the same problem with my top E if it is tuned perfectly as per the electronic tuner, it is out when I play a chord. I am using Elixir Mediums for the first, AND ONLY, time. I suspect that these strings are making the problem worse, as I find them a bit 'fat' and suspect the thickest string doesn't fit the groove in the nut properly. This changes the 'break over' angle to the headstock and might also decrease the amount of string in actual contact with the nut because of its poor fit in the nut groove.
I suspect in my case it is because of the guitar needing to be set up properly.
Giok