No, the Chernobyl reactor core is not still melting. The core meltdown occurred during the 1986 disaster, and the molten fuel eventually solidified into a mass known as the "Elephant's Foot." While this mass is still highly radioactive, it is no longer actively melting.
The "Elephant's Foot" is a solid mass of melted nuclear fuel mixed with concrete, sand, and other materials. It is located in the basement of the reactor building and continues to emit radiation. However, the melting process ceased long ago, and the core is now in a stable, solidified state.
The primary concern now is managing the ongoing radiation from the "Elephant's Foot" and ensuring the long-term stability of the sarcophagus that encases it.