  We present a study of the P-wave spin -triplet charmonium chi_{cJ} decays
(J=0,1,2) into pi^0 pi^0 pi^0 pi^0. The analysis is based on 106 million
\psiprime decays recorded with the BESIII detector at the BEPCII electron
positron collider. The decay into the pi^0 pi^0 pi^0 pi^0 hadronic final state
is observed for the first time. We measure the branching fractions B(chi_{c0}
-> pi^0 pi^0 pi^0 pi^0)=(3.34 +- 0.06 +- 0.44)*10^{-3}, B(chi_{c1} -> pi^0 pi^0
pi^0 pi^0)=(0.57 +- 0.03 +- 0.08)*10^{-3}, and B(chi_{c2} -> pi^0 pi^0 pi^0
pi^0)=(1.21 +- 0.05 +- 0.16)*10^{-3}, where the uncertainties are statistical
and systematical, respectively.
