What actually is the event that we think we have detected with gravitational waves? This answer shows the "event" that is creating excitement.  It looks to the untrained eye like a single "blip" on a detector.  It appears to last less than a second.
It is, later in the answer, referred to as a "black hole merger".
Are we seriously saying that two black holes merged in under a second?
 A: Yes - the black holes actually merged in less than a second. If my memory serves me from the press announcement, at the time of final collision, the two black holes were moving relativitistically, at approximately 50% the speed of light. When you have compact massive bodies orbiting one another with very small orbits, you get very high speeds.
A: The signal was fit to that produced by two black holes merging, with each having a mass of roughly 30 times that of our sun.  For a solar mass the Schwarzschild radius is about 3 km.  So that means the black holes, if off by themselves, would have an event horizon radius of about 90 km.
Only right near the end of their fate during the merger was the gravitational wave strong enough to make it above the detector noise threshold.  Yes gravitational waves were emitted during the entire process, but we can only detect the violent end which releases the strongest waves.
In the process of merging, the black holes were moving relativistically. So moving on the order of 100 km many times in that short chirp recorded is quite reasonable.
