Last year I grew my own fresh tarragon for the first time, and this was my favourite way to use it. Where it calls for fresh tarragon, definitely use it. If you use dried tarragon there, you're REALLY cheating yourself.
Season the chicken breast halves lightly (and I do mean lightly, as you don't want to overpower the tarragon), and place them in a saucepan large enough to spread them out in one layer. Pour over the wine and chicken broth (add more broth if neceesary to cover the chicken), and then add the dried tarragon and the garlic.
Bring to a simmer over medium heat and cook for about 10 minutes.
Using a slotted spoon, transfer the chicken to a plate and cover to keep warm.
Using a sieve, strain the cooking liquid into a small saucepan. Skim off that fat and boil until reduced by about two thirds or so. Really concentrate that flavour.
Add the heavy cream and boil to reduce the whole mixture by about half. Again, it's all about concentrating that flavour.
Slice the chicken into strips about one-inch thick, and then share out the sauce among each serving.