This paper introduces a new univariate flexible generator of distributions called the odd Chen-G family. Some of its statistical properties are derived. Two special models of the proposed generator are provided. The model parameters are estimated using six estimation methods, namely, maximum likelihood estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramér-von Mises estimators and percentile based estimators. Further, simulations are performed to compare their performances for both small and large samples. Finally, two real data sets are used to illustrate the flexibility of the special models of the proposed family.