In large, heavy bottomed pot render andouille sausage and ham over medium low heat until slightly crisp.
Use slotted spoon to remove sausage and ham from pot and reserve (will add back to pot later).
Strain rendered fat and add to a new saute pan. Keep original pot ready to use again later. Do not clean out pot. You will want all of the caramelized bits on the bottom of the pan to flavor the gumbo.
In clean skillet, heat rendered fat over medium-low heat. Add one cup of flour to the fat, whisking to incorporate.
Add more vegetable oil as needed until roux is a little thicker than the consistency of gravy.
Cook over medium-low heat while stirring CONSTANTLY until the roux becomes the color of peanut butter to dark chocolate, depending on your desired flavor. Do not let roux burn.
Once roux is at desired color, carefully transfer to an oven safe container. Put roux in refrigerator to cool.
Heat original pot to medium high. Add the trinity (onions, peppers, celery) and a small amount of oil, salt and pepper.
Cook trinity until the edges of the vegetables begin to brown.
Turn off the heat and stir in the minced jalapeno and garlic.
Season chicken thighs on both sides with salt and pepper.
Heat a separate saute pan on high. Add some oil and sear the chicken on each side.
Transfer seared chicken thighs to cutting board. Cool slightly and then cut into small dice. Add diced chicken to the pot that holds the previously cooked trinity.