Do the burning of unscented candles help in any way to reduce the
level of cigarette smoke or odour in a room? Is there a chemical
reaction that takes place?

Dear Blue Jay, 

There are several known methods to reduce the level of cigerette odour
in rooms, and none of them involves "regular" candles. No chemical
reaction could take place with the burning of regular candles except
for the further reduce of clean oxygen in the room.

As far as I know, scented candles can in fact reduce the odour of
cigarettes, including, especially specialised ones (scented ones, that
are also specialised to reduce cigarette odour). I must add here that
I had a roomie (and best friend), whose only fault was smoking like a
railway engine. That helps, but not enough, in cases of serious odour.

Several online shops sell unscented types, although I personally doubt
if they help - one of the reasons candles help is by spreading another
smell around - I give them here:
http://www.safehomeproducts.com/SHP/ES/Soot-free_candles.asp 
http://www.candlevision.com/candlevision.filereader?3dd73da8045d30c2271d424d361a0631+EN/products/ODR001011&2D3
("odor eliminator" scent).

There are several chemical solutions to the odour of cigarettes. The
most famous (commercially) is "Fabreeze". It is a spray you can use on
textiles, shoes, etc. - and get the odour out.

Zeolite is a biological element that reduces, according to its
marketers, the odour of cigarettes:
http://www.squirmy-worms.com/zeolite.htm

Other "granny medicines" include setting out a dish of viniger (see
http://www.wigwamen.com/newsletter/october2002.pdf, p. 5); and heating
up water with cinnamon or clover. Other suggestions: using apples
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&threadm=l5fhgc3txza.fsf%40qubit.eng.sun.com&rnum=1&prev=/groups%3Fhl%3Den%26lr%3D%26ie%3DISO-8859-1%26q%3Dodor%2B%2Bcigarette

My search strategy was to search for "odor OR odour" and cigarettes
and "unscented candles".

I hope that answers your question. Please contact me for any further
clarifications on the answer, before you rate it.

bluejay-ga,

Using my knowledge of high school chemistry ;), the burning of candles
wouldn't do a thing.  Since the fumes of cigarettes is the byproduct
of a combustion reaction, they certainly will not be consumed by the
candle.  Odourwise, nothing should happen except maybe the smell of
burning wax covering the smell of the cigarette smoke.  Which is bad. 
Since smoke is cancerous.  My advice is to avoid cigarette smoke
entirely.

-Tox-ga

Traditionally, burning white candles (only white) was always supposed
to remove the odour of cigarette smoke. My grandparents swore it
worked and neither of them smoked, however I can't find any documented
proof of this.

milamba-ga

Dear Bluejay - 
     
    This is strictly wifes tales kind of stuff but I heard that
burning candles ( white normally as they contain no pigment in them )
would reduce the actual smoke in the room.  Not the odor.

Morningstar