Easy. What you can do is prepare some other executable file, and then cp chmod over it.
$ cp /bin/ls chmod
$ cp /bin/chmod .
The first cp creates a file called chmod with executable permissions, but which is really the ls executable. The second cp populates this file with the binary code of chmod, while preserving the execute permissions of the target file (because we did not specify any options to carry over permissions of the source file).
Another approach is to use the install utility which is a glorified copying program which can set permissions in one step. (See the -m argument.)
$ install -m a+x /bin/chmod .
$ ./chmod # executes
The install program isn't part of the Unix specification, but it is found in BSD, and in GNU Coreutils. Both support the -m option with chmod-like syntax, both symbolic and octal.