Hi Peter,
Thanks for using ADI products on your applications. Where is your input voltage coming from? Can you make sure that it is not floating by ensuring the it is connected to a common ground where your reference pin is also connected? Also the part with a gain of 1 can go as high as 1 MHz bandwidth only as stated on its datasheet. You shouldn't expect to behave it accurately above 1 MHz bandwidth. Would it be possible for you to share your layout so that we can check if we are missing something?
Best regards,
Emman