Separate ladyfingers (or thinly slice cake) and lay pieces side by side (or overlap, as needed) to cover a 14- to 15-inch-wide rimmed platter or very shallow bowl; leave a 1-inch rim.
Mix chestnut spread with rum and 2 tablespoons of the orange syrup. Pour remaining syrup over ladyfingers to moisten evenly. Gently spread chestnut mixture over ladyfingers, leaving 1 inch at rim of the cookies uncovered.
In a bowl with a mixer on high speed, beat whipping cream until it holds distinct peaks; whisk in the yogurt. Swirl over chestnut spread and most of the exposed ladyfinger rim.
Pare chocolate with a vegetable peeler to make curls, or finely chop with a knife or in a food processor. Scatter chocolate over tiramisu. Top chocolate with orange slices. Scoop portions with a spoon.
Orange syrup: In a 1- to 1 1/2-quart pan over high heat, boil 1 cup water, 1/2 cup sugar, and 1 tablespoon finely shredded orange peel until reduced to 3/4 cup. Let cool slightly and add 1/4 cup rum or orange juice. Use hot or cool.