  The double zeta function was first studied by Euler in response to a letter
from Goldbach in 1742. One of Euler's results for this function is a
decomposition formula, which expresses the product of two values of the Riemann
zeta function as a finite sum of double zeta values involving binomial
coefficients. In this note, we establish a q-analog of Euler's decomposition
formula. More specifically, we show that Euler's decomposition formula can be
extended to what might be referred to as a ``double q-zeta function'' in such a
way that Euler's formula is recovered in the limit as q tends to 1.
