The dimming was far more irregular and dramatic than could be caused by a planet passing in front of the star - even a gas giant like Jupiter blocks only 1 per cent of the sun's light.
Other natural explanations, such as a cluster of comets swarming around the star, didn't fit the data for what became known as "Tabby's Star", for Boyajian.
So Jason Wright, a Penn State astronomer involved in SETI (Search for Extraterrestrial Life) research, proposed an unnatural explanation: a swarm of alien megastructures.
The dimming more or less matched what scientists might expect to see from a Dyson Sphere - a giant system of solar panels that an advanced alien civilisation might hypothetically use to harness energy from a star.
"It's never aliens" is a pretty time-honoured rule in astronomy. The history of science is rife with examples of phenomena that looked like evidence of extraterrestrials but turned out to be something much more mundane.
And Wright acknowledges it doesn't take extraterrestrial intelligence to make a star behave strangely.
But the teeny, tiny incredibly unlikely possibility that something is out there means that astronomers can't stop talking about Tabby's Star. And, regardless of the source, the dimming is worth understanding.
Which is why, when the celestial object began to flicker again last week, Wright, Boyajian and the rest of the astronomy community went mildly bananas.
Though a number of dimming events are documented in Kepler space telescope data, this was researchers' first chance to watch Tabby's Star flicker in real time.
That's a big deal, because it means scientists can target the star with a number of telescopes that operate at a variety of ranges across the light spectrum.
This will allow them to take spectra, that is, analyse the wavelengths of light emitted by the star to figure out what it's made of and what is blocking its light.
That data will be crucial to pinpointing the source of Tabby's Star's strange behaviour.
For example, if a swarm of disintegrating comets is causing the dimming, they'll be very hot and close to the star, and scientists will be able to see that in the infrared part of the spectrum, according to website the Verge.
Good quality spectra could also help test a theory that the star is in the act of messily devouring a Jupiter-sized planet.
Boyajian had predicted earlier that the star might act up again in May, and this month she was proved right.
Around May 20, the light from Tabby's Star dropped by as much as 3 per cent over a period of around 24 hours, Boyajian reported in a Q&A live stream. Now it's moving back toward normal.
"It looks like the dip has mostly ended," astronomer David Kipping of Columbia University told Science magazine. "But ... in the Kepler data we saw an episode of multiple dips clustered together over the span of a few weeks."
So far, this pattern of behaviour is similar to the events detected by Kepler, scientists said, so it's possible that the dimming is caused by a single object repeatedly crossing in front of the star.
As for the alien megastructure theory, it's still super unlikely. Scientists haven't detected any radio signals coming from that direction, even since they started listening with the massive Green Bank Telescope in West Virginia.
Whatever is happening on Tabby's Star, dozens of people living on a small blue planet 1300 light-years away (and 1,300 years later, because the light that is hitting us now left Tabby's Star in the 8th century), are intent on finding out.
Boyajian, now at Louisiana State University in Baton Rouge, told Science that the astronomy community seized on its chance to watch Tabby's Star in action.
Astronomers at a dozen different observatories took spectra over the course of just two days - some of them dropping their own ongoing projects to help.
"A physical interpretation of what's going on will take more work," Boyajian said.
"But the process has begun."
