Glider near miss with Airliner (emergency climb) near Chicago yesterday?

I was cross countrying in Brazil Central Plateau last week. As it was to be a long flight (9+ hours) and with scarce air traffic, I kept radio watch but transponder off.
When passing about 5 miles South of an untowered airport, I heard a descending exec jet, asked for his position and bearing and calculated we were going to cross paths, warned the jet pilot and turned on my transponder.
He deviated to the left after I appeared in his TCAS and crossed in front of the glider exactly in the same altitude...