Is the signal detected by LIGO a result of the merging of the horizons or the singularities? Regarding gravity waves, some YouTube videos show simulations of the gravity waves detected by LIGO in August of 2017.
Is the "chirp" the result of the merger of the event horizon or the merger of the singularities?
 A: The chirp is not due to the merging of horizons or singularities, but the whole system. But the chirp changes when the horizons meet.
Gravitational radiation is emitted if the quadrupole moment of a system changes at an accelerating pace. That means that it is due to the total distribution of mass rather than particular objects. The chirp happens because the two black holes orbit each other, producing a changing quadrupole, losing energy as radiation and hence approaching each other, getting into an ever faster whirl. When the two holes get close enough they merge. As can be seen in this simulation, the event horizon "jumps" to encompass both of them. At this point what is left is a highly deformed single black hole that wobbles, radiating away its quadrupole moment in the "ringdown phase". So the end of the chirp is marked by the horizon merger... somewhat.
When the horizons or singularities merge is somewhat undefined. There will be a moment when an observer sees the two holes topologically become one, but the light from this has had to escape a very steep gravity well and is delayed. In fact, even the horizon itself is somewhat tricky to point at since it is (just like a normal horizon) not an actual thing but a range from which beyond nothing can be seen. Even worse is the issue of "when" the singularities: inside a black hole the radial direction takes on characteristics of time and the singularities are essentially spacelike, so it might not even exist a proper connection between our external time and the internal meeting of singularities.
The thing to remember is that black holes are systems, extended curvatures of spacetime that do not end at the event horizon but in a real sense extends to infinity (or at least as long as their gravity can be noticed). It is just that the deformation is most obvious near the horizon. 
A: Neither.
While I largely agree with answer by Anders Sandberg, I would like to emphasize that neither horizon, nor singularity are directly responsible for gravitational waves observed, but instead all waves are produced by a  gravitational field strictly outside the merging horizons. By its very definition horizon is the surface from which no signal, including gravitational wave could escape. Merging horizons would not affect that one defining property. And singularities are even more inaccessible, hidden behind horizons. 
Observation of a chirp gives us information about the near horizon structure of a black hole for the distances of about $r_s \exp (- \frac{c \tau}{r_s})$ outside the horizon, where $\tau$ is the duration of the chirp (while it is distinguishable from the noise) and $r_s$ is the horizon radius of a merged black hole. While exponential function would approach zero rapidly, it would never quite reach it.
