Can a Chilean national who is in the U.S. apply to change status to H-1B1 while in the U.S.?

Yes. A national of Chile, currently admitted to the United States as a nonimmigrant in a category eligible to change nonimmigrant status, may apply to change to H-1B1 nonimmigrant status. Note that the applicant must be in the U.S. in a nonimmigrant category which is eligible to change nonimmigrant status, of course.