Hello, I am a US citizen by naturalization. I live in US and pay my taxes. I want to leave the country to live and work in another country for 3 years

If you are a naturalized U.S. citizen, you enjoy the same rights and responsibilities as a person who is born in the U.S.  If you have a U.S. passport you are entitled to travel subject to the same restrictions as any other U.S. citizen.  You don't abandon your citizenship by leaving the country.  The only way you can lose citizenship is if you lied on your application or if you renounce your U.S. citizenship. If, however, you are a lawful permanent resident "green card holder" then your status can be affected by travel, in which case, you should consult with am immigration attorney to determine whether your travel plans could jeopardize your status.