I've tried looking at Wikipedia but it is extraordinarily vague. Is it even known at all? I ask about this because I'm working on a very informal hypothesis about a period of common development between the Germanic, Celtic and Italic languages, but I would need to know when, more or less, they were spoken.
Looking at a few related wikipedia pages:
According to David W. Anthony, between 3100–2800/–2600 BCE, a real folk migration of Proto-Indo-European speakers from the Yamna culture took place into the Danube Valley. These migrations probably split off Pre-Italic, Pre-Celtic and Pre-Germanic from Proto-Indo-European.1
- David W. Anthony - The Horse, The Wheel and Language pg.344
Using a mathematical analysis borrowed from evolutionary biology, Don Ringe and Tandy Warnow propose the following evolutionary tree of Indo-European branches:23
- Pre-Celtic and Pre-Italic (before 2500 BCE)
David Anthony, following the methodology of Ringe and Warnow, proposes the following sequence:26
- Pre-Celtic and Pre-Italic (3000 BCE)
- Anthony 2007, pp. 56–58.
- Anthony 2007, p. 100.
Umbrian & Faliscan are both attested and distinct as far back as the 7th century BCE (i.e. the 600s BCE), so this gives us a terminus ante quem (a latest possible date)
PIE is generally accepted to have broken up somewhere around 4500-5000 years ago or 2500-3000 BCE (see the dates given in ukemi's answer) giving us a terminus post quem (an earliest possible date)
That leaves us with a window of 3000-700 BCE or so which isn't especially helpful. I'm not sure if archaeology can be used to help narrow this down, but I think assuming it's nearer the later part of that (i.e. Italic only became distinct from the post-PIE continuum relatively late, around the time it arrived in Italy) is relatively safe and lines up with the ca. 1000 BCE given on wikipedia. The main thing to bear in mind is that the "ca." is doing a lot of work there