Fumarate hydratase (FH) is an enzyme of the tricarboxylic acid cycle (TCA cycle) that catalyses the hydration of fumarate into malate. Germline mutations of FH are responsible for hereditary leiomyomatosis and renal-cell cancer (HLRCC). It has previously been demonstrated that the absence of FH leads to the accumulation of fumarate, which activates hypoxia-inducible factors (HIFs) at normal oxygen tensions. However, so far no mechanism that explains the ability of cells to survive without a functional TCA cycle has been provided. Here we use newly characterized genetically modified kidney mouse cells in which Fh1 has been deleted, and apply a newly developed computer model of the metabolism of these cells to predict and experimentally validate a linear metabolic pathway beginning with glutamine uptake and ending with bilirubin excretion from Fh1-deficient cells. This pathway, which involves the biosynthesis and degradation of haem, enables Fh1-deficient cells to use the accumulated TCA cycle metabolites and permits partial mitochondrial NADH production. We predicted and confirmed that targeting this pathway would render Fh1-deficient cells non-viable, while sparing wild-type Fh1-containing cells. This work goes beyond identifying a metabolic pathway that is induced in Fh1-deficient cells to demonstrate that inhibition of haem oxygenation is synthetically lethal when combined with Fh1 deficiency, providing a new potential target for treating HLRCC patients.