For 0 <= mu <= 2, let fmu(x)=1-mu*x^2. In its principal period-doubling cascade, let mu_n be the parameter at which the attracting cycle of least period 2^(n-1) has multiplier -1 and bifurcates to a cycle of period 2^n. Define delta=lim_{n->infinity}(mu_(n+1)-mu_n)/(mu_(n+2)-mu_(n+1)), the Feigenbaum delta constant. Is delta transcendental over the rational numbers?