When is a door not a door?  When it’s ajar.  This word is only used once in our text, at the crucial spot where Bilbo escapes the goblin mountain by squeezing through the door left slightly ajar.  The “a-” is preposition 1, expressing being in a situation.  But what situation?  “On char” is an  obsolete way of saying “in the act of turning or shutting” but not yet shut.  From “char” we get “chore” – an occasional turn of work.

• 05.142 It was still ajar,

“a, prep.1.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.

“ajar, adv.1 and adj.1.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.

“chare | char, n.1.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.