This paper presents a post-silicon hold time closure technique for performance-relaxed, sub-threshold digital designs using tunable-buffer insertion in hold-critical data-paths. Hold time closure in flip-flop based digital circuits is highly critical because hold failures cannot be corrected post-fabrication. This criticality increases in the sub-threshold domain, which is highly sensitive to process, voltage, and temperature variations. Design-time hold margins enable robust hold time closure across variations. However, insufficient hold margins can lead to chip failures and overestimated hold margins introduce additional costs in area and power. In this paper, we propose a post-silicon hold time closure methodology that introduces tunable-buffers in the data-path. This enables post-silicon correction of hold violations and therefore, reduces the design effort in estimating design-time hold margins. We design a tunable-buffer, demonstrate the tunable-buffer insertion strategy, and present a physical design flow using standard EDA tools. We verify this technique with measurements of a 130 nm test chip. A design-dependent hold slack improvement in the range of 103%-195% is achieved compared to the traditional buffering technique, with minimal power and area overhead. This technique also has the potential to reduce the number of buffers inserted for hold closure.