Large language models (LLMs) are known to produce outputs with limited diversity. In this work, we study whether infusing random concepts in the prompts can improve the diversity of the generated outputs. To benchmark the approach, we design a systematic evaluation protocol which involves prompting an LLM with questions of the form "Name 10 Hollywood actors", and analyzing diversity measures of the resulting LLM outputs. Our experiments on multiple LLMs show that prepending random words/sentences unrelated to the prompt result in greater diversity in the outputs of LLMs. We believe that this promising result and the evaluation protocol opens up interesting avenues for future work, such as how infusing randomness into LLMs could be applied to other domains. Further, the evaluation protocol could also inspire research into benchmarking LLM diversity more systematically.