Monitoring Round-Trip Time provides important insights for network troubleshooting and traffic engineering. The common monitoring technique is to actively send probe packets from selected vantage points (hosts or middleboxes). In traditional networks, the control over the network routing is limited, making it impossible to monitor every selected path. The emerging concept of Software Defined Networking simplifies network control. However, OpenFlow, the common SDN protocol, does not support RTT monitoring as part of its specification. In this paper, we leverage the ability of OpenFlow to control the routing, and present GRAMI, the Granular RTT Monitoring Infrastructure. GRAMI uses active probing from selected vantage points for efficient RTT monitoring of all the links and any round-trip path between any two switches in the network. GRAMI was designed to be resource efficient. It requires only four flow entries installed on every switch in order to enable RTT monitoring of all the links. For every round-trip path selected by the user, it requires a maximum of two additional flow entries installed on every switch along the measured path. Moreover, GRAMI uses a minimal number of probe packets, and does not require the involvement of the controller during online RTT monitoring.