Optimizing accuracy and performance while eliminating hallucinations of open-domain conversational large language models (LLMs) is an open research challenge. A particularly promising direction is to augment and ground LLMs with information from structured sources. This paper introduces Conversational Tables cTBLS, a three-step architecture to retrieve and generate dialogue responses grounded on retrieved tabular information. cTBLS uses Transformer encoder embeddings for Dense Table Retrieval and obtains up to 125% relative improvement over the retriever in the previous state-of-the-art system on the HyrbiDialogue dataset. cTBLS then uses a shared process between encoder and decoder models to perform a coarse+fine tabular knowledge (e.g., cell) ranking combined with a GPT-3.5 LLM response generator to yield a 2x relative improvement in ROUGE scores. Finally, human evaluators prefer cTBLs +80% of the time (coherency, fluency) and judge informativeness to be 4x better than the previous state-of-the-art.