The Defence Secretary told a conference fringe event the £70 million annual running costs would have to be found by cutting something else.
The first of the 920ft-long vessels, weighing 65,000 tonnes is under construction at Rosyth Dockyard in Fife.
The second, HMS Prince of Wales is also under construction at shipyards across the United Kingdom.
Mr Hammond said the costs involved in bringing the second ship into full service were small given the cost of building it.
Previously announced plans had suggested the HMS Queen Elizabeth would come into service on completion, but the Prince of Wales could be kept back pending a decision at the 2015 Strategic Defence and Security Review (SDSR).
Mr Hammond said: "It's got to be a decision for the SDSR. My recommendation would be we should try to support the use of the second carrier.
"I think having put the money we have into building the carriers, for the sake of about £70 million per year being able to operate the second carrier looks like a snip.
"But it does mean we have to stop doing something else. If we spend an extra £70 million a year to be able to operate two carriers, which gives us a guaranteed one permanently available to go to sea, if we do that we will have to stop doing something else.
"All these things are about choices and priorities, what are we going to give up in order to do something that needs to be done."
Queen Elizabeth will be the lead ship of the class of aircraft carrier and is scheduled to start sea trials in 2017.