The ground level in Pozzuoli, Italy, at the center of the Campi Flegrei caldera, was monitored by tide gauges between 1970 and 1976 and then continuously since 1982. Tide gauges offer a long record of a variable that is believed to be related to the activity of an underlying shallow magma chamber. Previous work suggests that the dynamics of the Campi Flegrei system, as reconstructed from the tide gauge record, is chaotic and low dimensional. According to this suggestion, in spite of the complexity of the system, at a time scale of days the ground motion is driven by a deterministic mechanism with few degrees of freedom; however, the interactions of the system may never be describable in full detail. Our new analysis of the tide gauge record from January 1987 to June 1989, using Nonlinear Forecasting, confirms low-dimensional chaos in the ground elevation record at Campi Flegrei and suggests that Nonlinear Forecasting could be a useful tool in volcanic surveillance.