Accurately modeling lifetime data is very important for appropriate decision making in health and biomedical fields. This usually requires the use of distributions. However, no single distribution can model all types of data. Hence, the development of distributions with appropriate usefulness is very important for modeling purposes. In this study, a new lifetime distribution, known as Chen Burr-Hatke exponential distribution is proposed. The objective of the study is to obtain a new lifetime distribution which can serve as an alternative distribution to modeling lifetime data. Also, such a distribution can be used to provide inferences via regression models. Plots of the density function of the new distribution show that the distribution can exhibit increasing, decreasing, right-skewed and left-skewed shapes. Also, plots of the hazard rate function show that the distribution can exhibit increasing, decreasing, and upside down bathtub shapes. Statistical properties, such as the quantile function, moments, order statistics and inequality measures, are derived. Several estimation methods are used to estimate the parameters of the distribution. Using Monte Carlo simulations, the estimators were all consistent. However, maximum likelihood estimation method was observed to better estimate the parameters of the distribution. Two regression models based on the distribution are established. The usefulness of the distribution and its regression models are demonstrated using real lifetime datasets. The results show that the models can provide a good fit to lifetime data, and hence can serve as alternative models to fitting such data.