I just had a crash due to hitting a dog. My carbon fiber frame now has chip the size of a dime at the junction of the seat stay and drop out on the drive side. Should I be concerned about frame failure now or in the future?
Anytime you are in a crash I think you need to be worried about damage to the frame and future frame failure. Unfortunately it's very difficult for a lay person to inspect and evaluate damage to a carbon frame. For this reason I would suggest that you take the frame to a reputable bike shop and have it inspected there.
You should also remember that carbon fiber absorbs water, so the chip in your paint/gel coat get should be fixed ASAP, as water damage can cause a corrosion cell to form and the frame to fail.
Assuming the frame passes the inspection of the bike shop, you can touch up the damage with clear coat touch-up paint, or some people have used clear fingernail polish.