That's what some right-wing MPs have suggested in parliament.
Swiss People's Party (SVP) MP Erich Hess spoke out against the system of dual nationality, which currently allows foreigners to keep their original nationality when they become Swiss citizens, reported 20 Minutes.
Those who keep their original nationality may not be fully committed to Switzerland, said Hess, adding they “should choose which country they love” to prove they are well integrated.
He also criticized the fact dual nationals get benefits that regular Swiss citizens do not get, for example they can more easily get work permits and welfare benefits in their second country of citizenship.
However the MP's words were derided by others, including Liberal-Radical Cedric Wemuth, who said it would be “absurd” to force people to choose Switzerland over their foreign nationality, reported 20 Minutes.
“There are people who are linked to several countries. That doesn't make them bad Swiss,” he said.
Having citizens with double nationality can even be an advantage for Switzerland, he added, saying that often dual nationals spread a positive image of Switzerland in their ‘other' nation.
Some other European countries including Austria do force foreigners to renounce their current citizenship when they are naturalized.
The debate arose in the Swiss parliament ahead of a referendum on February 12th when the Swiss public will vote on whether to make it easier for third generation immigrants to become Swiss.
That initiative is strongly opposed by the SVP and their allies, some of whom have fought a combative campaign with controversial posters showing a woman in a burqa. Critics of the posters argue they are misleading because the new law would mostly concern non-Muslim Italians who have lived in Switzerland their whole lives and are well integrated.
Unlike in some other countries, citizenship is not automatically conferred on a person who is born in Switzerland. Therefore if a person's grandparents were immigrants, and their parents did not obtain Swiss citizenship, third generation immigrants could have been born in Switzerland and have lived here their whole lives without having Swiss citizenship.
They can of course apply for it, but are subject to the same stringent conditions and lengthy process as everyone else.
The February 12th referendum aims to decide if this process should be made simpler for them.