Parametric resonators that show large amplitude of vibration are highly desired for sensing applications. In this paper, a microelectromechanical system (MEMS) parametric resonator with a flexible support that uses electrostatic fringe fields to achieve resonance is introduced. The resonator shows a 50% increase in amplitude and a 50% decrease in threshold voltage compared with a fixed support cantilever model. The use of electrostatic fringe fields eliminates the risk of pull-in and allows for high amplitudes of vibration. We studied the effect of decreasing boundary stiffness on steady-state amplitude and found that below a threshold chaotic behavior can occur, which was verified by the information dimension of 0.59 and Poincaré maps. Hence, to achieve a large amplitude parametric resonator, the boundary stiffness should be decreased but should not go below a threshold when the chaotic response will appear. The resonator described in this paper uses a crab-leg spring attached to a cantilever beam to allow for both translation and rotation at the support. The presented study is useful in the design of mass sensors using parametric resonance (PR) to achieve large amplitude and signal-to-noise ratio.