Season the chicken with salt and pepper. Heat a large pot with a lid or a Dutch oven over medium-high heat with olive oil, 2 turns of the pan. Brown chicken on each side then remove to a plate. Add ham to the pan and brown the cubes, 2-3 minutes; remove to a plate.
Add butter to pot and melt. Add leeks and garlic, and season with salt and pepper. Cook to soften, 3-5 minutes. Deglaze the pan with wine, scraping up the bits at bottom of pan. Whisk up stock, Worcestershire and mustard, and pour into pan. Add potatoes, carrots, chicken and ham, and cover.
Cook in a 325F oven or over a medium-low flame for 40-45 minutes, stirring occasionally.
To serve, halve the lemon and squeeze the juice around the pan; garnish with lots of tarragon.