The famous series of Fibonacci numbers is defined by a recursive equation saying that each number is the sum of its two predecessors, with the initial condition that the first two numbers are equal to unity. Here, we show that the numbers of fatty acids (straight-chain aliphatic monocarboxylic acids) with n carbon atoms is exactly given by the Fibonacci numbers. Thus, by investing one more carbon atom into extending a fatty acid, an organism can increase the variability of the fatty acids approximately by the factor of the Golden section, 1.618. As the Fibonacci series grows asymptotically exponentially, our results are in line with combinatorial complexity found generally in biology. We also outline potential extensions of the calculations to modified (e.g., hydroxylated) fatty acids. The presented enumeration method may be of interest for lipidomics, combinatorial chemistry, synthetic biology and the theory of evolution (including prebiotic evolution).