Peel shrimp and reserve shell for the shrimp broth. Transfer the shrimp to a bowl, cover, and refrigerate them until the chowder base is completed. Place the shrimp shells in a large pot and add 10 cups of cold water. Bring to a simmer over high heat, then reduce to low and gently simmer for 5 minutes, skimming off any foam that rises to the surface. Strain the broth through a fine sieve and set aside.
Cook bacon in a small pot of simmering water for 1 minute. Drain. Heat a medium pot over medium heat; add the bacon and cook, stirring occasionally, until it releases some of its fat. Add potatoes and leeks, stir well, then reduce heat to medium-low and cook, covered, stirring occasionally, for 5 minutes. Add 3 cups of the reserved shrimp broth (freeze remainder for another use) and simmer, covered, until potatoes are tender, about 8-10 minutes. Remove the chowder base from the heat and cover to keep warm.
Melt butter in a large skillet over medium-high heat. Raise the heat to high, add the chilled shrimp and cream, stir well, and bring to a boil. Let boil for 30 seconds.
Add the shrimp mixture to the chowder base and stir gently to combine. Cover and let rest for 10 minutes. Season with salt, a generous amount of black pepper, and the cayenne. Ladle into warm soup bowls and sprinkle the chives on top.