I've successfully repaired several similar broken concrete steps, although none as old as yours, and probably several hundred concrete bridge abutment and pier corners. The trick is to first remove (by careful grinding) any high spots in the exposed base concrete. It's best not to try to remove material from the underside of the broken-off piece, as you may fracture it. A small masonry wheel will work just fine, and is a lot less expensive than a diamond grinder someone suggested. Make sure all of the base concrete is clean, tight and sound--anything that sounds hollow when you drag a hammer over it has to be removed by judicious use of a geologist's pick. You want to remove as little material as possible, otherwise you may wind up with an epoxy layer more than a half inch thick (not good). Sand blasting is the best treatment for ensuring good bond of the epoxy, but a vigorous wire brushing can be just as effective for such a small area. Give the area (both the base and chunk to be glued down) a good scrubbing with water and a stiff bristle brush, then either blow it dry with oil-free compressed air or just let it air dry.
Go to a masonry supply place, and pick up a small kit of low modulus, high viscosity epoxy (sometimes referred to as a gel, most of them are a light gray color when mixed). Thoroughly mix the 2 components, and apply a thin layer on both surfaces to be bonded. Press the piece into place, making sure some of the gel is squeezed out along the entire bonding surface--you don't want any voids that can collect water and freeze, causing the patch to break free in the winter. Work a little powdered Portland cement and graphite dust into the visible bonding surfaces after you've scraped away all excess epoxy, which will make the epoxy blend in better with the color of the adjacent concrete once it cures.