Integrated Sensing and Communication (ISAC) requires the development of a waveform capable of efficiently supporting both communication and sensing functionalities. This paper proposes a novel waveform that combines the benefits of both the orthogonal frequency division multiplexing (OFDM) and the chirp waveforms to improve both the communication and sensing performance within an ISAC framework. Hence, a new architecture is proposed that utilizes the conventional communication framework while leveraging the parameters sensed at the receiver (Rx) for enhancing the communication performance. We demonstrate that the affine addition of OFDM and chirp signals results in a near constant-envelope OFDM waveform, which effectively reduces the peak-to-average power ratio (PAPR), a key limitation of traditional OFDM systems. Using the OFDM framework for sensing in the conventional fashion requires the allocation of some resources for sensing, which in turn reduces communication performance. As a remedy, the proposed affine amalgam facilitates sensing through the chirp waveform without consuming communication resources, thereby preserving communication efficiency. Furthermore, a novel technique of integrating the chirp signal into the OFDM framework at the slot-level is proposed to enhance the accuracy of range estimation. The results show that the OFDM signal incorporated with chirp has better autocorrelation properties, improved root mean square error (RMSE) of range and velocity, and lower PAPR. Finally, we characterize the trade-off between communications and sensing performance.