We present an investigation of the Lagrangian dynamics of a hurricane from the perspective of using micro aerial vehicles (MAVs) or small unmanned aircraft systems as mobile sensors for hurricane research and monitoring. The low cost of MAVs allows the use of more sensors for volumetric in situ measurements, particularly in high-risk locations where larger more expensive systems cannot be used. However, the limited flight speed of MAVs enforces severe restrictions on potential flight plans. In the face of 70-m/s horizontal winds, a MAV with only 10-m/s flight capability has very little directional control. Fortunately, vertical wind speeds in the hurricane are much lower and have limited spatial extent. Using Lagrangian coherent structure techniques and simplified vehicle simulations, we develop an understanding of the transport dynamics of a simulated hurricane and apply this understanding to a high-level control scheme to enable MAV navigation and guidance near the hurricane. By smartly adjusting their altitude, simulated MAVs are able to navigate into the hurricane eye at a very high success rate. Our findings suggest that the smart use of the existing background flow could allow the use of low-cost sensor platforms in extreme environments.