Can a Java class be called from within a CICS COBOL program running under Enterprise Server?

The answer is "no" you cannot call Java objects directly from COBOL using the Java OO methods. You can, however, accomplish this in a different manner. You can start a separate process in the COBOL program running under Enterprise Server and start up a multi-threaded COBOL .EXE that does the calls to the Java classes.

Parameters can be passed back and forth using calls to CBL_ALLOC_SHMEM, CBL_PUT_SHMEM_PTR and CBL_GET_SHMEM_PTR (see Net Express docs)

The run-unit can be started using CBL_EXEC_RUN_UNIT (see Net Express docs.)