Separate the chicken skin from the meat of the chicken with a forefinger. Do not try to pull the skin away from the breast bone or from the back, as it may tear.
Remove the tarragon leaves from the stems and place them between the skin and meat of the chicken.
Truss the chicken and place it in a tight-fitting, tall but narrow pot. Pour over just enough of the chicken stock to cover the chicken.
Slowly bring the stock to a simmer, skimming off any froth that floats to the surface. Poach the chicken for approximately 40 minutes. Transfer it to a plate and cover it lightly with foil to keep warm.
Reduce the poaching liquid while skimming carefully, until 1½cups (375milliliters) remain.
Add the cream to the reduced poaching liquid and whisk in the potato purée a bit at a time, until the sauce has the desired consistency. The sauce can be left very light—almost the consistency of a soup—or made thick enough to coat the pieces of chicken. For a very thin, light-textured sauce, strain through a chinois.
Remove and discard the skin from the chicken, carve the meat, and serve it with the sauce in hot bowls or wide deep plates.