It is very important to know the chill requirements when selecting a fruit tree. My area usually receives between 600 and 700 chill hours on average, which is why I wouldn't plant Red Delicious apples (1400 chill hours) or Redglobe Peaches (850 chill hours).
If a tree doesn't receive enough chill hours, it will be slow to break dormancy, have reduced fruit set (or none at all), and the fruit quality is lower. It's OK if the tree receives more chill hours, but at a minimum most trees need to receive their specific chill requirements to be healthy and productive.
The Texas A&M Horticulture website gives two ways to estimate the accumulated chill hours of an area, based on readily available weather data. The first method uses the mean January temperature to chill, and the second method uses the average of the mean December and January temperatures:
January Mean Method:
Estimated Chill Accumulation = 3547-54 x (January Mean Temperature)
December/January Mean Method:
Estimated Chill Accumulation = 4280-68.8 x (December+January mean temperature/2)
However, it is important to note that these methods do not consider late cold snaps in February, like the one we had this year. I used both methods to estimate the chill hours my area received for the past 20 years, and the results are surprisingly variable. Even though my area receives and average of 600 chill hours, a Red Baron peach tree would only receive it's full chill requirement roughly 60% of the time. Much better to plant something with a chill requirement of less than 400 hours, like Midpride or Tropic Snow.