Assessing and managing cloud risks can be a challenge, even for the cloud service providers (CSPs), due to the increased numbers of parties, devices and applications involved in cloud service delivery. The limited visibility of security controls down the supply chain, further exacerbates this risk assessment challenge. As such, we propose the Cloud Supply Chain Cyber Risk Assessment (CSCCRA) model, a quantitative risk assessment model which is supported by cloud supplier security assessment (CSSA) and cloud supply chain mapping (CSCM). Using the CSCCRA model, we assess the risk of a Customer Relationship Management (CRM) application, mapping its supply chain to identify weak links, evaluating its security risks and presenting the risk value in dollar terms, with this, promoting cost-effective risk mitigation and optimal risk prioritisation.