The deeper an arrow is embedded in the chest, particularly the upper chest (where all the great vessels are) the more likely you are to do major, unsurvivable damage considering your era. To answer this question more fully, I’d want to know the size of the arrow. How long and wide is it? I would think anything measuring an inch or more would be worrisome for nicking something important like a large blood vessel or the lung. The way around this might be to have the person be fairly overweight and the arrow gets embedded into fat tissue. This might not be a good option for your hero.