A political “war chest” is the amount of money a political candidate or a political party has raised to spend in an election (“the war”). A physical “chest” is not required to store the money; a political bank account can be a “war chest.” 
   
The political version of the term “war chest” has been used since at least the 1880s, perhaps first in Great Britain.
   
   
Wikipedia: War chest
In business, a war chest or cash mountain is a stash of money set aside to deal with unexpected changes in the business environment, or to use when expansion possibilities arise. The term originates with the medieval practice of having a chest, literally, filled with money to open in time of war.
 
Today companies can use accumulated cash or rely on quickly raised debt which costs less to carry when you don’t need it. This is not always a reasonable substitute, as the debt available to a company typically drops as a result of the same actions that require the war chest to be opened.
 
Companies can redistribute their war chests to shareholders by issuing larger or special dividends, or more commonly through share buyback operations. Companies do this because if actually held in cash, the companies will be earning a low rate of return in the money markets, whereas they could be using the funds to invest in more profitable projects. If they continue not to invest the funds, shareholders may sell the company’s shares and make it vulnerable to a takeover. This would place the current management’s jobs at risk.
 
This term is also used in other contexts. In politics it refers to the stash of money that a candidate or party has to use for an anticipated election campaign. In football it refers to the amount of money a manager has been given by a club’s chairman, owner or investors to acquire new players, as in the newspaper headline, “Defoe and Brown top Keegan wishlist as Ashley grants £25m war chest”.
 
War chests are also referred to as surplus cash, cash reserves, emergency reserves, acquisition funds, rainy day funds, or undistributed earnings within different contexts.
 
Merriam-Webster’s Online Dictionary
Main Entry: war chest
Function: noun
Date: 1871
: a fund accumulated to finance a war; broadly : a fund earmarked for a specific purpose, action, or campaign
     
(Oxford English Dictionary)
war chest, (a chest or strong box for) funds used in waging war; freq. used fig., esp. of funds used by a political party to finance an election campaign
1901 CORVO Ho. Borgia 34 The papal jewels were pawned, and their price added to the *war-chest.
1912 W. DEEPING Sincerity xvi. 124 He had about forty pounds left, no great sum to start a war-chest with.
1932 Sun (Baltimore) 30 Aug. 1/6 (heading) War chests practically empty, parties curtail on campaign.
1973 R. L. SIMON Big Fix iv. 34 All the guilt-stricken celebrities contributing to their war chest.
 
14 April 1887, Macon (GA) Weekly Telegraph, “Votes Openly Bought; How the Charter Election in Jacksonville was Carried,” pg. 4:
In Monday’s election it was determined to fight the devil with fire. It was known that the gamblers and liquor men had liberally replenished their war chest, abd that some of the regulars were openly boasting that “Burbridge’s barrel wasn’t big enough.”
 
30 July 1888, Baltimore (MD) Sun, “Topics in New York - Political Notes,” pg. 1:
The visitors are numerous from all sections of the country, and many handsome contributions to the war chest have already been made.
     
23 January 1895, Newark (OH) Daily Advocate, pg. 3, col. 3:
In the first place, if he had formed any such intention, he would hardly be likely to make it public, because, in the second place, any such announcement would have a disastrous effect upon the party war chest. (...)—London Figaro.
 
Google Books
A History of Politics
By Edward Jenks
New York, NY: The Macmillan Company
1900
Pg. 137:
Election fights.—Most people, probably, have noticed that the language of elections is somewhat bloodthirsty. We speak of the “party war-chest,” the “election campaign,” the “enemy’s stronghold,” “laying siege to a constituency,” “leading troops to victory,” “carrying the war into an opponent’s territory,” and so on.
 
Google Books
Corruption in American politics and life
By Robert Clarkson Brooks
New York, NY: Dodd, Mead and Co.
1910
Pg. 201:
Under present conditions the party organisation with strongly centralised management has a direct interest in limiting corruption and also in seeing that contributions which arise from such practices as it tolerates actually flow into the party war chest.
 
Google Books
Democracy and the party system in the United States, a study in extra-constitutional government
By M. Ostrogorskiĭ
New York, NY: Macmillan Co.
1910
Pg. 352:
Great stress has been laid within the last few years on the limitation of contributions to campaign funds, which supply the Machines with a very large part of their war-chest.