Pricing in the rough Heston model of Jaisson & M. Rosenbaum [(2016) Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, The Annals of Applied Probability 26 (5), 2860–2882] requires the solution of a fractional Riccati differential equation, which is not known in explicit form. Though numerical schemes to approximate this solution do exist, they inevitably require significantly more time to compute than the closed-form solution in the classical Heston model. In this paper, we present a simple rational approximation to the solution of the rough Heston Riccati equation valid in a region of its domain relevant to option valuation. Pricing using this approximation is both fast and very accurate.