Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add the onion, bell pepper, and celery; sauté for 6 minutes until the vegetables are softened.
Stir in the minced garlic, Cajun seasoning, and cumin; cook for 1 minute until highly fragrant.
Add the diced chicken to the pot and cook for 5 minutes, stirring frequently until the exterior is browned.
Pour in the chicken stock, drained white beans, and diced green chilies; bring the mixture to a rolling boil.
Reduce the heat to medium-low and simmer uncovered for 25 minutes to allow flavors to meld and the liquid to reduce slightly.
Stir in the heavy cream and continue to simmer for an additional 5 minutes.
Remove the pot from the heat and stir in the lime juice and chopped cilantro.
Taste and adjust seasoning with salt and pepper as needed before serving.