According to the OED, a still-room is 'a room in a house in which a
still was kept for the distillation of perfumes and cordials', and later
'a room in which preserves, cakes, liqueurs, etc. and tea. coffee, etc.
are prepared'.  The two useages (which, to me, seem to be quite
distinct) are not separated out by the OED.  The first recorded useage
is 1710.  The second useage seems to be there by the early 1800s.  One
quotation is noteworth: a quote of 1858 says 'a century ago, every lady
in the country had her still-room and medicine chest'.  That medical
useage is there in the earlier use of still-room: a cordial is not a
kind of fruit squash or syrup: it is a heart stimulant.

'Still' in 'still-room' is not (directly) an aphetic (reduced) form of
'distill': the noun 'still' was formed from the now obsolete verb 'to
still' (meaning 'to trickle down or fall in minute drops').  To _still_,
first recorded over 200 years before the 'still', is the aphetic form of
'distil'.  There is no recorded use of 'distill-room'.

--
Pat Reynolds
(who wants to live in a still-room, later useage)
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at home
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at work
Keeper of Social History, Buckinghamshire County Museum
   "It might look a bit messy now, but just you come back in 500 years time"
   (T. Prattchet)