This test chip demonstrates an ultra-low-power crystal (XTAL) oscillator design that generates a 32.768 kHz clock for real-time clock applications. An inverting amplifier operational from 0.3 V VDD oscillates the XTAL resonator and achieves a power consumption of 2.1 nW. At such low voltages of operation, the negative resistance and power consumption of the amplifier can show variation with process. At some process corners, the amplifier can consume higher power and give very high negative resistance; and at other process corners, its negative resistance can be low, and it may fail to meet the oscillation criteria. A calibration circuit addresses this variation using which we bias the amplifier with a fixed current. The digital controller implements a duty-cycling technique that powers down the XTAL amplifier without losing the oscillation and reduces the power consumption to 1.5 nW. The XTAL oscillator design is implemented in 130 nm CMOS with an area of 0.0625 mm2 and achieves a temperature stability of 1.85 ppm/¬∞C.