A skill is an ability that has been acquired by training.
With the demands of Customer Service being what they are, ie, irrate customers, high quality expectations of service delivery, customer complaints etc, I would say the most important skills one should have include, good communication skills, tolerance, understanding and above all patience.
These skills go two ways, both when dealing with customers and when dealing with your team/subordinates.
Most importantly, you should love what you do. I would say you need to be an individual who loves talking to people, otherwise the demands of Customer Service will seem much more complex. Being a 'people' person is an added skill/advantage.
I hope my suggestions will be of help to you.
All the best and always expect Success.