Add mayo, sour cream, heavy cream, oil, salt, and pepper to a blender or to the bowl of a food processor. Process/blend on high until smooth.
For a SMOOTH dressing: Add the chives and all of the crumbled blue cheese. Pulse until combined and completely smooth.
For a CHUNKY dressing: Add the chives and half of the crumbled blue cheese. Pulse until combined but not completely smooth. Stir in the rest of the blue cheese crumbles.
Store in a glass jar in the fridge for up to 2 weeks.