Cut the chicken fillets into strips. Season with patis and pepper.
Cut off the skin of the squash, scoop out the seeds and cut into one-inch cubes.
Peel, crush and finely mince the garlic.
Peel and finely slice the onion.
Peel and cut the ginger into thin slices (grating the ginger works too).
Slice the tarragon — finely, if you prefer; coarsely if you want them to be really visible and add color to the cooked dish.
Heat the cooking oil in a pan. Add the chicken and cook until the edges start to brown (they’re almost done at this point). Add the ginger, onion and garlic, and saute until fragrant, about a minute. Add the cubed squash. Season with more fish sauce and pepper. Stir well.
Pour in about a cup of chicken broth, add the tarragon, and stir once more. Bring to the boil, lower the heat, cover and simmer for about ten minutes or until the squash is done.
If you're having the tarragon chicken with squash for a home meal, serve immediately. If you're packing it in a lunchbox, cool slightly before sealing the container.