How can alcohol be removed from an alcohol-containing drink (such as
beer or wine) in a way that the drink will become alcohol-free?

Method should be:
Using chemical reaction(s) which would be adding one or more
substances to the drink.

If suggesting a compound:
Include the name of each substance used.
How the substances were made into the compound.

You must also:
Include the chemical reactions which will take place once the
substance(s) are added to the drink.

The drink must:
Remain safe, acceptable and legal to drink.
 
The chemical reaction must:
Not make the cold drink hot.
Not produce too much gas.
Not be too slow (take hours)

Please note:
You must give the names of substances and the process of reactions
using approved scientific language.
Make sure that the information you give is correct and practical.

I this homework? Sounds like it to me.

It may be possible to remove the alcohol with a chemical reaction, but
I have my doubts about how "acceptable" the result would be.  It is
certainly not the preferred method:
http://sheknows.com/about/look/1789.htm
http://www.drinks-business-review.com/article_news.asp?guid=E5369AEE-2E2B-4633-ACE8-9AD18D0D75C2
http://www.freepatentsonline.com/4775538.html
http://www.traveltastes.com/dealcohol.htm

Wine vinegar. Yum, yum.

I had a look on the internet and found that:
Acetobacter is a bacteria commonly used to convert alcohol to acetic
acid (vinegar). Oxygen encourages its growth and that is why it is
important to exclude oxygen at all times during the wine making
process.
Unfortunately, this is not a fast enough reaction and also no one
likes to buy wine or beer and end up drinking a glass of vinegar and
bacteria instead!

I hope that some one will be able to come up with the right answer, if
there is one. :-)

There are a few chemical reactions which I know can turn an alcohol
into something else but I am not sure if any of these would be useful
here. You might find them interesting anyway.

Carboxylic acids are week acids which can be formed by oxidising a
primary alcohol to an aldehyde and then to a carboxylic acid. Aldehyde
will need to be refluxed with an oxidising agent such as potassium
dichromate to produce the carboxylic acid.

The aldehyde can react with Fehling?s solution and produce a red
copper I oxide precipitate.

Small aldehydes burn completely with oxygen and release water and carbon dioxide. 

This might mean that the aldehyde in the solution will burn away
slowly using the dissolved oxygen. Whether a splint / flame is needed
or not to start the reaction would depend on the activation energy
required to start the burning reaction of  aldehyde with oxygen.

If a carboxylic acid is heated with an alcohol in presence of acid
catalyst an esterification reaction will produce an ester such as
ethyl ethanoate and water.

Esters have a sweet smell and are sometimes used as food flavourings.

Sodium or potassium hydrogencarbonate reacts with a carboxylic acid to
produce a milky solution of water and carbon dioxide.
RCOOH + NaHCO = RCOONa + WATER + CARBON DIOXIDE

Carboxylic acids can also react with alkalis such as NaOH to form
salts such as sodium ethanoate and water.

A carboxylic acid can be turned into an acyl chloride by reacting it
with phosphorus pentachloride or sulphur dichloride oxide. The acyl
chloride can then react with an alcohol at room temperature to produce
an ester. This is faster than esterification but produces some HCl
(acid) too.

Acidified potassium dichromate (VI) oxidises a primary alcohol to
produce a carboxylic acid and changes the colour of solution from
orange (dichromate VI ion) to green (chromium ion). A secondary
alcohol would result in production of a ketone instead.