Dice potatoes into "fat" quarters. Slice each potato in half lengthwise, then each half widthwise.
Place potatoes into a large 6-quart pot (they need room to move). Add enough cold water to cover the potatoes by about two inches.
Place the pot over high heat and bring the water to a boil. Add the kosher salt, then reduce the heat to medium-high. Boil until the potatoes are tender and can be easily pierced with the tip of a knife, 8-10 minutes.
While the potatoes are cooking, make the vinaigrette. Combine the extra virgin olive oil, red wine vinegar, lemon juice, lemon zest, garlic, parsley, and chives in a small bowl or 1-cup measuring cup. Whisk until the dressing is emulsified.
Drain the potatoes, shake to release as much water as possible, then place the potatoes back into the hot pot. The heat from the pot will help any residual water dissolve.
Pour the vinaigrette over the potatoes, then toss to coat. Taste for seasoning and add additional salt or pepper as needed.
Marinate at room temperature for at least 1 hour, and up to 4. Serve at room temperature, and enjoy!
