This is a pretty fast op-amp. It's almost certainly due to layout or decoupling.
Do you have ceramic decoupling caps right at the supply inputs to a ground plane? Is this on a PCB with short traces and a tight layout or is it on a breadboard?
If it's the latter you might want to try a lower bandwidth op-amp. Since your differential gain is 1 but your noise gain is 2, you need an amplifer with a gain bandwidth of say 10MHz or so. (Assuming the 1MHz signal is the highest frequency you need to work with.)
This is a 300MHz amplifier, which is probably making your life more difficult than it needs to be.