Fermilab experiment E835 has observed (-)pp annihilation production of the charmonium state chi(c0) and its subsequent decay into pi(0)pi(0). Although the resonant amplitude is an order of magnitude smaller than that of the nonresonant continuum production of pi(0)pi(0), an enhanced interference signal is evident. A partial wave expansion is used to extract physics parameters. The amplitudes J=0 and 2, of comparable strength, dominate the expansion. Both are accessed by L=1 in the entrance (-)pp channel. The product of the input and output branching fractions is determined to be B((-)pp-->chi(c0))xB(chi(c0)-->pi(0)pi(0))=(5.09+/-0.81+/-0.25)x10(-7).