I dont think brining is your problem. Overcooking the chicken breasts might be. You didn't give us much info on the recipe. You did tell us skinless chicken breast, but that tells us its bone-in since you didn't say boneless.
It makes a difference. Either way, an hour is generally considered too much time by most recipes. Boneless runs about 20-25 minutes in the oven and bone-in runs about 30-35 minutes. The biggest mistake most people make is overcooking chicken breast. It's best removed from the heat at 160° and allowed to rise to 165°, just barely into the "safe zone". The tiniest bit of pink on the bone is OK with bone-in breasts as long as the meat itself is not still pink and running blood anywhere. It's the temp at the fattest part of the breast that matters most.
Also, did you rinse the chicken and most importantly, pat it dry? Browning in white wine doesn't sound right either, typically a recipe would have you brown in a fat like butter and oil THEN pour in the wine or broth to de-glaze and begin the braising process or rest of the recipe. Chicken breast is not an ideal meat for braising but can be baked really good...just not for an hour usually. That's going to nearly guarantee tough chicken...when using breast.
If you want to share the recipe you were working from, I can try to help tweak it for another try if you'd like.
Something I do, whether I'm grilling, sauteing or baking is pound the "boneless" breast to an even thickness. Not necessarily thin, just so the whole breast is around the same thickness. I dont use bone-in breasts for anything in the last, at least 20 years. I have no use for them...even with fried chicken...let the women have those and the kids the drumsticks, the thighs are the prize!
