For the paella: Add the chicken stock, saffron threads and shrimp shells to a medium saucepan and simmer, covered, for 10 minutes.
Meanwhile, coat the paella pans generously with olive oil. Add the chorizo, dividing it between the two pans. Set the pans over medium-low heat and cook, stirring occasionally, until the fat has rendered and the chorizo is crispy, 5 to 7 minutes. Add the chicken to the pans and season with salt. Cook, stirring occasionally, until the chicken is beginning to brown, but isn’t cooked all the way through.
Add the garlic, celery, onions, peppers and tomato to a food processor and pulse until chopped into a coarse paste. Add to the paella pans and cook until all of the liquid has evaporated and the veggies are soft and slightly caramelized, about 10 minutes. Add the peas and cook 2 to 3 minutes.
Add about 1/2 cup of the stock to each pan and stir, making sure to scrape up the fond from the bottom of the pans. Season to taste with salt. Add about another cup of the stock to each pan, then bring the liquid to a boil.
Add the rice and stir until thoroughly combined. Nestle the clams into the rice and cook for 5 minutes. Nestle the shrimp into the rice and simmer until the shrimp are pink and cooked through and the clams have fully opened, 5 minutes.
For the aioli: Meanwhile, add the vinegar, garlic and egg yolks to a food processor and process until combined. With the machine running, slowly add the oil to emulsify the mixture. Season to taste with salt.
For serving: Garnish with the chives and a drizzle of aioli.