Since chlorine is quite a heavy element (heavier elements are produced in lesser quantities by stars), the star which produced enough chlorine to create a whole chlorine world/planet must have been a 9 solar masses+ blue supergiant star. This star exploded in a supernova and from its remains (the nebula) this planet could have formed.
Chlorine gas is not a very good greenhouse gas, meaning that your planet would not be a blistering world unless it was quite close to the parent star. Or if you prefer to have CFCs in the atmosphere instead of pure chlorine, then yes, you do get a highly greenhouse atmosphere with a large heat reserve.
A planet with an atmosphere primarily composed of chlorine is indeed possible, considering that there is nothing which makes it impossible to form. However, such a planet cannot be of a gas giant size. It would be a terrestrial planet (most probably Mars sized) with vast amounts of chlorine-containing chemicals in its crust. These chemicals either suffer decay or are processed (by organic processes) by microbes to release the chlorine in them.