Can we make any implications about the internal structure of black holes from the 'chirp' that LIGO observed? Are there any implications about a black hole's internal structure we can make based on the chirp issued? For example that a black hole does in fact contain or does not contain a singularity rather than a super-dense form of matter/energy that we can't otherwise discover anything about due to the event horizon and information paradox?
 A: 
Are there any implications about a black hole's internal structure we can make based on the chirp issued?

No. The chirp data is consistent with the waves generated by the spacetime outside of two merging black holes. Therefore if there are two black holes, we'd get that data. Similarly if there were two compact and time dilated bodies such that the spacetime outside them were very very similar to the spacetime outside a black hole, then we'd get the same data (no data is perfect, so if the compact and time dilated body had a spacetime outside that was similar enough we'd get literally the same data).

For example that a black hole does in fact contain or does not contain a singularity rather than a super-dense form of matter/energy that we can't otherwise discover anything about due to the event horizon and information paradox?

Waves don't come from inside the horizon, so we don't learn anything about the inside of the horizon. We don't even learn whether there is an inside to the horizon, let alone what, if anything, might be going on inside. We learn about the outside.
We learn that the outside is similar to the outside of a black hole. So the outsides of compact bodies are very similar (or possibly identical) to the outsides of black holes and produce waves like the outsides of black holes produce.
A: Gravitational waves are produced outside the black hole event horizon.
Background One of the ways LIGO conducts their search for gravitational waves is by using templates, so they match the known waveforms coming from binary black hole (or other compact object) systems with what is expected from theory.
The story After they made the initial estimates for the parameters, they ran a supercomputer simulation (which shows pretty well where the gravitational waves are generated) to verify the results.
What they can theoretically infer:


*

*Lower limit for the mass of the graviton

*Mass of the binary black holes

*Spin

*Future observations: Velocity of gravitational waves (speed of light, fingers crossed)

