If the card is stolen, a chargeback will be issued and you will be out of pocket. This is an inherit part of ecommerce however there are things you can do to limit your exposure.
There's a legal gap that you can maneuver around in terms of when you receive the order and when you ship it. It's tight and sometimes chargebacks occur over a month later.
The other things you can do are; don't ship to certain countries, don't ship if the card address doesn't match the shipping address (the card address is sent to you in PayPal's IPN), don't process unusual orders.
The other side of things is that if you can get an IMA (internet merchant agreement), most payment processors such as Elavon and Realex have very sophisticated anti-fraud technologies, including the ability to use 3D Secure and SecureCode for Visa and MC respectively.