A chemical property is a property that is associated with chemical reactions and changes in the composition of matter. Examples of chemical properties are heat of combustion, flammability, toxicity, etc. A physical property, on the other hand, is something that can be measured or sensed, without changing the composition of the matter. Examples of physical properties include, melting point, density, volume, mass, etc.
Radioactivity is the defined as emission of radiations from an unstable nucleus. These particles can be alpha, beta and gamma particles. Uranium-238 exhibits radioactivity by release of an alpha particle and the reaction can be written as:
`U^238 _92 -> Th^234 _90 + He^4 _2`
In this reaction, we can see that uranium converts to thorium, i.e. the composition of the matter changes. And hence by the definition of chemical and physical properties, radioactivity is a chemical property.
Hope this helps.