Very much depending on the vintage, because they select and sell off the rest, but I guess J.L.Chave bottles between 25.000 and max. 50.000 bottles of (Domaine-)Hermitage per vintage, app. 2/3 red, 1/3 white.
That´s definitely more than La Tâche, but much less than Lafite-R. …
I used to spend more time in the southern rhone, generally part of road trip vacations. Having only seen/heard of Chave through movies or social media, I decided to drive up and see if I could get any. I actually managed to find some (2012/2013 vintages) at the only open shop in Tain l’Hermitage. At 235eur, not quite the local bargain I was hoping for but hey, I scored a couple bottles…!