Has any modern country gained independence peacefully?

Yes, many times, and that is the rule of the modern era, not the exception. The idea that independence must mean war is a relic. Since the Second World War, the world has watched a steady stream of peaceful, negotiated separations, several of them between settled democracies that simply decided to go their own ways. Texas would be joining a well-worn path, not blazing a dangerous new one.

The modern record is a wave, not a war

The scale of it is easy to miss. Since 1945, more than 130 new countries have taken their place among the nations of the world, and the overwhelming majority did so without anything resembling the American Civil War. The United Nations had 51 member states at its founding. It has 193 today. That growth is the story of peoples around the globe taking up self-government, most of them peacefully, through negotiation, treaty, and the ballot box. Independence is one of the most common political events of the last eighty years.

Two free countries split with a handshake: Norway and Sweden, 1905

For a case that looks remarkably like Texas, go back to 1905. Norway had been in a union with Sweden, and it decided to leave. The Norwegian parliament moved first, the Norwegian people then confirmed it in a plebiscite that passed with nearly unanimous support, and the two governments negotiated the terms at Karlstad. Sweden recognized Norway as an independent nation that same year. Two stable, democratic, European neighbors dissolved a union by vote and negotiation, with no war. More than a century ago, free people were already doing peacefully exactly what Texas proposes.

A textbook clean break: the Velvet Divorce, 1993

Closer in time, Czechoslovakia separated into the Czech Republic and Slovakia on January 1, 1993. The split was negotiated by the leadership of both sides and settled in law by their parliament over a matter of months. It was so calm and so free of conflict that history named it the Velvet Divorce. International recognition followed within weeks, and both nations went on to become stable democracies and members of the European Union. It is the cleanest example in modern memory of a peaceful national separation by mutual consent.

A nuclear superpower dissolved without civil war: the USSR, 1991

If anyone insists a large, heavily armed state cannot come apart peacefully, history answers directly. In 1991 the Soviet Union, a nuclear superpower, dissolved into fifteen independent nations. The Baltic states reestablished their independence, the leaders of Russia, Ukraine, and Belarus signed an accord recognizing one another's sovereignty, and the rest followed within weeks. As one Russian official later put it, the Soviet Union broke up without a civil war, thank God. The largest state on Earth ended without the war the doubters always predict.

The pattern holds, and Texas fits it

These are not cherry-picked oddities. They are the normal way the modern world redraws its lines. The lesson across all of them is the same: when there is consent and a willingness to negotiate, separation is peaceful. War comes from refusing to negotiate, not from the act of separating. Texas, with its developed institutions, its enormous economy, and a process built on a lawful vote, fits the peaceful pattern far better than it fits the violent exception people keep reaching for.

The bottom line

Peaceful independence is not a hope. It is the documented norm of the last eighty years, from Norway and Sweden to Czechoslovakia to the breakup of the Soviet Union. Texas would be following the rule, not breaking it.