The goal of any radiation treatment plan is to achieve maximal disease response with minimal toxicity. HDR brachytherapy offers a promising definitive treatment option in the setting of Locally Recurrent Prostate Cancer after prior definitive radiation, based on the limited data described above, with achievement of biochemical disease control in a large percentage of patients with relatively low toxicity. With focal HDR brachytherapy, the investigators can treat the isolated areas of disease, while avoiding normal prostate tissue, with the goal of further improving toxicity rates. The investigators hypothesize that using single fraction, focal HDR brachytherapy performed with one single implant for the treatment of LRPC is feasible and without excess toxicity, and can be safely delivered. This should allow for better patient convenience and cost and improved treatment dosimetry and planning, as it will decrease the risk of catheter displacement between fractions, which will hopefully correlate to less GU and non-GU acute toxicity. The primary objective is to determine the acute and late GU and GI toxicity of single fraction focal HDR salvage brachytherapy (primary endpoint).