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A porous-core photonic crystal fiber based on a cyclic olefin homopolymer (Zeonex) is proposed; it shows high birefringence, high core power fraction, low losses, and near-zero flat dispersion. The fiber’s core was designed with quad-elliptical (QE) air holes with its center occupied by bulk background material. The superiority of the QE design over the commonly adopted tri- and penta-elliptical (TE and PE) core designs is demonstrated. The presence of the bulk material at the core center and the geometrical configuration cause a broad contrast in phase refractive indices, thereby producing high birefringence and low transmission losses. A high birefringence of 0.096 was obtained at 1.2 THz, corresponding to a total loss of 0.027 cm−1 and core power fraction of approximately 51%. The chromatic dispersion and effective area of the reported fiber were also characterized within a frequency range of 0.4–1.6 THz. The QE air holes were then filled with chemical warfare agents, namely, tabun and sarin liquids. Then, the relative sensitivity, confinement loss, fractional power flow, and effective material loss (EML) of the sensor were calculated. Nearly the same relative sensitivity (r = 64%) was obtained when the QE core was filled with either liquid. Although the obtained EML for tabun was 0.033 cm−1 and that for sarin was 0.028 cm−1, the confinement loss of the fiber when it was immersed in either liquid was negligible. The proposed fiber can be fabricated using existing fabrication technologies. Moreover, it can be applied and utilized as a THz radiation conveyor in a terahertz time domain spectroscopy system for remote sensing of chemical liquids in the security and defense industries.