Under the influence of the COVID-19 pandemic and the concurrent oil conflict between Russia and Saudi Arabia, oil prices have exhibited unusual and sudden changes. For this reason, the volatilities of the West Texas Intermediate (WTI), Brent and Dubai crude daily oil price data between 29 May 2006 and 31 March 2020 are analysed. Firstly, the presence of chaotic and nonlinear behaviour in the oil prices during the pandemic and the concurrent conflict is investigated by using the Shanon Entropy and Lyapunov exponent tests. The tests show that the oil prices exhibit chaotic behavior. Additionally, the current paper proposes a new hybrid modelling technique derived from the LSTARGARCH (Logistic Smooth Transition Autoregressive Generalised Autoregressive Conditional Heteroskedasticity) model and LSTM (long-short term memory) method to analyse the volatility of oil prices. In the proposed LSTARGARCHLSTM method, GARCH modelling is applied to the crude oil prices in two regimes, where regime transitions are governed with an LSTAR-type smooth transition in both the conditional mean and the conditional variance. Separating the data into two regimes allows the efficient LSTM forecaster to adapt to and exploit the different statistical characteristics and ARCH and GARCH effects in each of the two regimes and yield better prediction performance over the case of its application to all the data. A comparison of our proposed method with the GARCH and LSTARGARCH methods for crude oil price data reveals that our proposed method achieves improved forecasting performance over the others in terms of RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) in the face of the chaotic structure of oil prices.