This article investigates the chaotic relationship among inflation rate, unemployment rate and oil prices over the period of January, 1974-October, 2018 in the USA. This study complements the previous studies on this subject. However, it differs from the existing literature in examination of inflation-unemployment trade-off by a neural network model in which oil prices are considered as an exogenous variable, and in analyzing the chaotic causality relation among the variables by Hristu-Varsakelis and Kyrtsou and Bai nonlinear causality tests. The results first suggested by a class of neural network model, which was the multi-layer perceptron (MLP), pointed out an important relation among the analyzed variables. Accordingly, oil price changes have substantial effect on unemployment and inflation. Following, the empirical findings of Hristu-Varsakelis and Kyrtsou and Bai nonlinear causality tests show that there is a unidirectional chaotic relation from oil price to inflation, from oil price to unemployment and from inflation to unemployment.