Line a cookie sheet with parchment paper and put a wire rack on top.
Combine sugar and water in a small saucepan; bring to a boil, stirring to dissolve the sugar. Reduce the heat to medium and simmer for 3 minutes. Add apricots and gently simmer 5 minutes. Transfer the apricots with a slotted spoon to the rack. Let cool completely. They should not be wet when dipping them.
Melt chocolate in a double boiler of simmering water. Dip half of a poached apricot in the chocolate, letting excess drip off. Sprinkle with chopped pecans over the chocolate half and return the apricot to the rack. Repeat with the remaining apricots. (You will have some melted chocolate left over.) Refrigerate until the chocolate has set, about 20 minutes.