Degenerate microwave amplifiers offer the potential to perform a measurement of weak mi- crowave signals free from any degradation to their signal-to-noise ratio, a benefit afforded by the quantum mechanics of their phase sensitive gain . The degenerate parametric amplifier may even be used to enhance the signal-to-noise ratio of a weak measurement by squeezing the vacuum fluctuations below the standard quantum limit. Consequently, parametric amplifiers have featured in a number of recent sensitivity breakthroughs across multiple fields. These include the detection of gravitational waves , the search for dark matter , and high sensitivity electron spin resonance spectroscopy . In this thesis, we present a novel microwave degenerate parametric amplifier based on the non-linear superconducting phenomenon of kinetic inductance. The device is a simple and robust quantum limited phase sensitive amplifier, which is well described by theory and shows potential as a highly-effective tool for the production of squeezed microwave light.