In this paper, we model the chemical evolution of a 0.25 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ protoplanetary disc surrounding a 1 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ star that undergoes fragmentation due to self-gravity. We use Smoothed Particle Hydrodynamics including a radiative transfer scheme, along with time-dependent chemical evolution code to follow the composition of the disc and resulting fragments over approximately 4000 yrs. Initially, four quasi-stable fragments are formed, of which two are eventually disrupted by tidal torques in the disc. From the results of our chemical modelling, we identify species that are abundant in the fragments (e.g. H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$O, H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$S, HNO, N$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$, NH$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$, OCS, SO), species that are abundant in the spiral shocks within the disc (e.g. CO, CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$, CN, CS, H$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$CO), and species which are abundant in the circumfragmentary material (e.g. HCO$\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$). Our models suggest that in some fragments it is plausible for grains to sediment to the core before releasing their volatiles into the planetary envelope, leading to changes in, e.g., the C/O ratio of the gas and ice components. We would therefore predict that the atmospheric composition of planets generated by gravitational instability should not necessarily follow the bulk chemical composition of the local disc material.