In a large bowl, whisk the mustard with the vinegar. Whisk in the canola oil in a thin stream and season with salt and pepper.
Bring 2 medium saucepans of salted water to a boil. Add the potatoes to one and cook for 20 minutes.
Cook the leeks until transparent, add the peas and cook until warmed but still vibrant green. Drain any excess liquid and pat dry; add to the vinaigrette. Drain the potatoes and slice 1/2 inch thick; add to the bowl.
Add the chives, season with salt and pepper and gently toss the salad. Serve warm.