Context is any information used to characterize the situation of an entity. Examples of contexts include time, location, identity, and activity of a user. This paper proposes a general context-aware DBMS, named Chameleon, that will eliminate the need for having specialized database engines, e.g., spatial DBMS, temporal DBMS, and Hippocratic DBMS, since space, time, and identity can be treated as contexts in the general context-aware DBMS. In Chameleon, we can combine multiple contexts into more complex ones using the proposed context composition, e.g., a Hippocratic DBMS that also provides spatio-temporal and location contextual services. As a proof of concept, we construct two case studies using the same context-aware DBMS platform within Chameleon. One treats identity as a context to realize a privacy-aware (Hippocratic) database server, while the other treats space as a context to realize a spatial database server using the same proposed constructs and interfaces of Chameleon.