A Chinese researcher’s claim that he successfully modified the genes of human embryos may force the country to make a stark choice about the future of its burgeoning biotechnology industry — one with significant implications for an emerging technology arms race with the West.

He Jiankui, an American-educated scientist based in Shenzhen, announced on Nov. 26 that he’d used Crispr, a powerful gene-editing tool, to make recently born twin girls resistant to HIV. He’s statement, which was not backed by...