About coming to the USA?

If a person who is from russia, decides to get duel citizensip to the czech republic......... can they mess up theeir chances of coming to the US and becoming a citizen... or... with them having citizenship in the czech republic, will this allow that person to come to the us without having to have a Visa... considering you do not have to have a visa to come to the US if you are from the Czech Republic......... Will having duel citizenship ruin someones chance of obtaining a citizenship here?