Gather the ingredients.

In a large pot, bring the stock to a boil with the shrimp shells and corn cobs. Cover and simmer for 30 minutes.

Remove the cobs. Strain the stock through a fine sieve into a large, heatproof bowl, pressing on the shells to remove as much stock as possible. Wipe out the pot.

In a small skillet, toast the celery and fennel seeds over moderately high heat until fragrant and starting to pop, about 45 seconds. Let cool completely. In a spice grinder or mortar, grind or crush the seeds to a powder.

In the large pot, melt the butter over moderately high heat. Add the yellow pepper, onion, celery, and chile and cook until they begin to soften, about 2 minutes. Add the ground fennel and celery seeds and cook for 1 minute.

Add the potatoes and shrimp stock and bring to a boil. Cover and simmer until the potatoes are tender, about 8 minutes. Remove from the heat.

Stir the shrimp and crabmeat into the chowder. Cover and let stand until the shrimp turn pink on the outside, about 3 minutes. Stir in the heavy cream and corn kernels. Bring to a simmer over moderate heat; immediately reduce the heat to low and simmer gently until the shrimp are white throughout, about 3 minutes. Season to taste with salt and pepper.

Ladle the chowder into bowls and garnish with chives. Serve with buttered toast.