The feasibility and potential performance of optical clocks based on all-optical atom chips using neutral strontium atoms have been investigated. The key benefits of all-optical atom chips are their ability to trap alkali-earth atoms, and how easily these atoms can be manipulated and examined. The planar configuration of the chip enables ring photonic resonators to be incorporated into its structure, making it a promising candidate for active optical atomic clocks. Using the 'magic wavelengths' of the trapping optical fields (813 nm and 390 nm for strontium atoms) minimises frequency shifts in the intercombination clock transition caused by variations in optical field intensity. However, this frequency shift can be compensated for using optical AC Stark shifts, which are generated by the trapping optical fields and have frequencies below the 'magic frequencies'. Furthermore, it has been demonstrated that atom chip clocks can operate using solely repulsive, blue-detuned evanescent light fields when the attraction of the trapped atoms towards the photonic waveguide is realised through van der Waals forces alone. According to estimates, this could result in the short-term fractional frequency stability of the strontium atom-chip optical clocks being limited to ~10^-16 per second, with an accuracy of about 5 x 10^-15 for fractional intensity stability in the trapping light fields of 0.001.