The last time I checked there is nothing on github's TOS page stating that your code must be open source. You could, hypothetically, include a LICENSE stating

The last time I checked there is nothing on github's TOS page stating that your code must be open source. You could, hypothetically, include a LICENSE stating that while the code is public, it is still copyrighted. Of course, I'm assuming if you have legal/contractual restrictions against open source, those restrictions also apply to making code publicly viewable.