Yes. These are the reasons you should have peace of mind:
1. Spree makes use of Peach Payments, a PCI-DSS Level 1 certified transaction platform and credit card storage vault to securely process your transaction. Read more about Peach Payments here. Spree does not have access to your card details.
2. The entire Spree website is served via a secure, private connection using HTTPS.
3. Spree supports 3D Secure, which is a new method of security mandated by the Visa and Mastercard Associations. 3D Secure provides an extra layer of security by requiring that the cardholder submits a second level of authentication when shopping online. It is managed by South African banks to enhance security of online transactions. Mastercard's product is called "SecureCode" and Visa's product is called "Verified by Visa".