setting a foreign key to an empty string
There are two approaches you can take
APPROACH #1 : Add to professor table
INSERT INTO professor (PROFID) VALUES ('');

Then, all INSERTs to DEPTCHAIR will work.
APPROACH #2 : Disable Foreign Key Check
SET foreign_key_checks = 0;
INSERT INTO DEPTCHAIR (PROFESSORID, DEPTID)
VALUES ('', 'BIO');
SET foreign_key_checks = 1;