We report on the inscription of fibre Bragg gratings (FBGs) in CYTOP (cyclic transparent optical polymer) optical fibres. A femtosecond laser beam, operating in the visible wavelength range, is focussed into the core of the fibre for direct inscription of FBGs. The fibre is moved under the focussed beam by a nanometre-resolution air-bearing stage for maximal inscription precision. The grating plane dimensions (measured with bright field microscopy) are typically 30μm × 30μm × 1μm (line by line grating) or 10μm×1μm×1μm (point by point grating) and centred in the core of the fibre for optimal grating efficiency. The FBGs have a typical reflectivity of 70%, a bandwidth of 0.25nm and an index change of ~10-4. The FBG operate in the C-band, where CYTOP offers key advantages over poly (methyl methacrylate) optical fibres, having a significantly lower optical loss in the important near infra-red (NIR) optical communications window, with a theoretical loss of ~0.3dB/km at 1550nm. Additionally, CYTOP has a far lower affinity for water absorption and a core mode refractive index that coincides with the aqueous index regime. These properties offer several unique opportunities for polymer optical fibre sensing at NIR wavelengths, such as compatibility with existing optical networks, the potential for optical fibre sensor multiplexing and suitability for bio-sensing. We have investigated the temperature response of the grating: a linear positive shift of ~ +40pm/K has been measured with little difference between the heating and cooling response. The strain response of the FBG has also been studied with a linear shift of ~ +1.3pm/μɛ measured over a few hundreds of μɛ. We also demonstrated compatibility with a commercial Bragg grating demodulator.