A tree structure is often used in wireless sensor networks to deliver collected sensor data to a sink node. Such a tree can be built using directional antennas as they offer considerable advantage over the omni-directional ones. A tree is adequate for data gathering from all sensor nodes as long as no node in the tree fails. Since the connectivity of the tree is one, failure of any one node disconnects the tree and may disable the sink node from collecting data from some of the sensor nodes. In this paper we study the problem of enhancing the fault tolerance capability of a data gathering tree by adding a few additional links so that the failure of any one sensor would not disconnect the tree. Assuming that the addition of each link to the tree involves some cost, we study the problem of least-cost augmentation of the tree, so that even after failure of a single node, all the surviving nodes will remain connected to the sink node. We prove that the least-cost tree augmentation problem is NP-complete. Moreover, we provide an approximation algorithm with performance bound of two. The experimental evaluations of the algorithm demonstrate that the approximation algorithm performs even better in practice and almost always produces near-optimal solution.