Blacksmith

The Blacksmith's house is located in the Light World east of Kakariko Village. The path is due east of the Kakariko Tavern.

Quest

To perform this quest, you must first save the Frogsmith. He's located south of the Village of Outcasts. The Titans' Mitts are required to release him from his prison. If you have the Magic Mirror, you can walk back to the location of their house, Mirror back, and enter their home.

If you do not have the Magic Mirror, you'll need to Save & Quit to return to the Light World.

Once he rejoins his partner, you need to leave the house, re-enter, and pay 10 Rupees to receive their item.

Upon completing that quest, the Purple Chest becomes available.