The pressure dependence of the sound velocities, single-crystal elastic constants, and shear and adiabatic bulk moduli of a natural gahnite (ZnAl2O4) spinel have been determined to ~9 GPa by gigahertz ultrasonic interferometry in a diamond anvil cell. The elastic constants of gahnite are (in GPa): C11 = 290(3), C12 = 169(4), and C44 = 146(2). The elastic constants C11 and C12 have similar pressure derivatives of 4.48(10) and 5.0(8), while the pressure derivative of C44 is 1.47(3). In contrast to magnetite, gahnite does not exhibit C44 mode softening over the experimental pressure range. The adiabatic bulk modulus KS0 is 209(5) GPa, with pressure derivative KS′ = 4.8(3), and the shear modulus G0 = 104(3) GPa, with G′ = 0.5(2). Gahnite, along with chromite (FeCr2O4) and hercynite (FeAl2O4) are the least compressible of the naturally occurring oxide spinels. Evaluation of Birch’s Law for isostructural minerals indicates that spinels containing transition metals on both the A and B sites follow a trend about five times more negative than oxide and silicate-spinel phases without any, or only one transition metal.