Lagopus has most of that covered.
The proof mark for 'CHOKE' came in in 1887, replacing 'NOT FOR BALL'. I would place your gun between 1887 and 1896.
The barrels look to be two iron damascus.
It was made with standard 2 1/2" chambers and 13 bore, as has been said, shows the bores were originally close to two proof sizes smaller than your gun now measures. The next proof up would be 13/1 (.719)and then 12 (.729)the next one up would be .740. This means the gun is currently out of proof.
The wall thickness will be a key factor, so get them measured. In my experience these guns were made with quite thick barrels - up to a minimum of 40 thou in many cases, so you may be pleasantly surprised.
As an observation, barrels of this period marked 'CHOKE' seem to have been made with what we now generally consider 'Modified' or 'three-quarter' choke constriction.
