Michael Schoch, Noodle Intern
It looks like three years-old is the youngest a child can be and attend public preschool in the Boston Public School district. BPS offers K0, K1, and K2 for children ages 3,4, and 5 respectively. This means you will have to wait at least until February 2016.
Dr. William Henderson Elementary has a K0 program for three year-olds. To learn more, I'd recommend calling the school at (617) 635-8725.
I hope this helps and best of luck to you!