HFT is arbitrage. The ask in Chicago falls below the bid in New York, so you buy for $12.25 in Chicago and sell for $12.27 in New York until there is either nobody willing to sell for $12.25 in Chicago or nobody willing to pay $12.27 in New York anymore. Which happens almost immediately, so whoever is fastest gets the money.
That means you want to be sitting right on both of the exchanges, but also that you want the fastest possible link between New York and Chicago.
Its for the people doing trades between exchanges (eg: New York to London) that this will benefit as they can act on the movement of another exchange before anyone else can. There is at least one microwave link between Chicago and New York to do this as the speed of light in air is faster than in glass.
That means you want to be sitting right on both of the exchanges, but also that you want the fastest possible link between New York and Chicago.