A novel physical phenomenon has been observed following the interaction of an intense (10(19) W/cm(2)) laser pulse with an underdense plasma. Long-lived, macroscopic bubblelike structures have been detected through the deflection that the associated electric charge separation causes in a proton probe beam. These structures are interpreted as the remnants of a cloud of relativistic solitons generated in the plasma by the ultraintense laser pulse. This interpretation is supported by an analytical study of the soliton cloud evolution, by particle-in-cell simulations, and by a reconstruction of the proton-beam deflection.