We demonstrate how LLMs can be harnessed to synthesize runtime verification monitors from natural language specifications. We instruct the LLM through prompts to assemble the monitors through a sequence of stages. To start with, we employ the learned insights LLMs possess regarding linear temporal logic for translating natural language specifications into propositional past time LTL formulas. Next, we utilize a sequence of prompts to synthesize from the LTL specification a runtime verification monitor for the given formula. Part of these prompts enable the LLM to validate its own outputs, thereby significantly improving the probability of obtaining a correct monitor.