Giant radio halos are Mpc-size sources found in some merging galaxy clusters .
The synchrotron emitting electrons are thought to be ( re ) accelerated by plasma turbulence induced by the merging of two massive clusters .
Cool core galaxy clusters have a low temperature core , likely an indication that a major merger has not recently occurred .
CL1821+643 is one of the strongest cool core clusters known so far .
Surprisingly , we detect a giant radio halo with a largest linear size of \sim 1.1 Mpc .
We discuss the radio and X-ray properties of the cluster in the framework of the proposed models for giant radio halos .
If a merger is causing the radio emission , despite the presence of a cool-core , we suggest that it should be off-axis , or in an early phase , or a minor one .