Heat olive oil in a large pot over medium heat.
Add chopped onion and sauté until translucent.
Stir in the garlic and cook for another minute.
Add diced carrots and cook for 5 minutes.
Incorporate the cubed potatoes and ham into the pot.
Pour in the chicken broth and bring to a boil.
Reduce heat and simmer for 20 minutes, or until potatoes are tender.
Stir in the heavy cream and season with salt and pepper.
Continue to cook for an additional 5 minutes.
Serve hot, garnished with fresh chives.