This paper presents an electronically adjustable memristor emulation circuit consisting of only two MOS transistors and a current source. The proposed circuit is topologically very simple, and it allows the memristor emulator to be realized without any external capacitor by using solely the transistor's internal capacitor. As a result of this, the circuit takes up little space on the IC environment. A modification technique based on using a negative immittance converter is used to operate the memristor in locally active region. The validity of the theoretical study is demonstrated by simulation results using the Cadence design environment with 0.18 mu m CMOS process and a possible application of the proposed MEC in a chaotic oscillator is presented. The feasibility of the circuit is also verified with experimental results.