Just to beat this to death, http://m.esa.int/Our_Activities/Space_Science/Gaia/Frequently_Asked_Questions_about_Gaia notes:
What will be included in the first public data release?
Gaia Data Release 1 includes the positions and G magnitudes – a broad,
visible light passband spanning 330 nm to 1050 nm – for more than one
billion stars using observations taken between 25 July 2014 and 16
In addition, for a subset of data – about 2 million stars in common
between the Tycho-2 Catalogue and Gaia – there will be a
five-parameter astrometric solution, giving the positions, parallaxes,
and proper motions for those objects. This is referred to as the
Tycho-Gaia Astrometric Solution (TGAS).
By measuring the amount of displacement – the parallax angle – and
knowing the distance between the Sun and the Earth, astronomers can
determine the star’s distance using simple trigonometry.
Even for the nearest stars the amount of apparent movement is tiny:
less than one arcsecond. Yet Gaia will measure the positions of one
billion stars to microarcsecond accuracies.
Assuming "will measure the positions" means "will measure the parallaxes", this appears to be referring to the final version of GAIA which will be published in the early 2020s.
To make things easier, http://cdn.gea.esac.esa.int/Gaia/ has a "tgas_source" subdirectory which just includes the 2,057,066 stars for which there is additional data (so you don't have to download the entire much larger GAIA archive).