The recently discovered Pr-based skutterudite superconductor PrOs₄Sb₁₂ was studied by means of low-temperature measurements of the thermal expansion coefficient \alpha along the cubic (100) direction of a single crystal sample in magnetic fields up to 8 T. Two superconducting phase transitions were found with critical temperatures T_c1=1.84 K and T_c2=1.71 K. Their hydrostatic pressure dependencies calculated using the Ehrenfest relation are -250 \pm 50 mK/GPa and -450 \pm 70 mK/GPa, respectively. For B \geq 5 T, we observe a thermodynamic phase transition which is presumably due to the onset of quadrupolar order. The transition temperature shifts with increasing B towards higher temperatures. The strongly enhanced value of the Gruneisen parameter \Gamma  provides clear evidence for the occurrence of a heavy-fermion normal state. The pronounced change of  \Gamma  at T_c provides evidence for the formation of Cooper pairs out of the heavy quasiparticles.

PACS numbers: 71.27.+a, 74.70.Tx, 75.30.Mb, 74.25.Dw