So not only do we have a superposition of observables, we also have a superposition of causality, in which the order of events happening is also in a quantum superposition.
This evidence has been experimentally observed in a new paper published in Science Advances this past week. See the press release here.
What they appear to have developed is this more robust "causal witness" that allows them to sample the superposition without destroying the coherence of the system.
Now, despite the headlines of the press release and the so-called implications, this isn't a result that destroys causality. What I seem to gather here is that, in the case where there is an uncertainty on which event occurs first, i.e. the causal order itself is in a superposition, then it is only upon a measurement will we get to know which comes first, the chicken or the egg. After that, things follows as usual. This experiment shows evidence that, yes, chicken followed by egg, and egg followed by chicken, are both there before a measurement.
 G. Rubino et al., Sci. Adv., 3, e1602589 (2017).