In a sample of 3.02 million hadronic Z0 decays collected by the DELPHI detector, 270 View the MathML source candidates have been selected. A search for fully reconstructed Bc± mesons has yielded one View the MathML source candidate, no View the MathML source candidates, and one View the MathML source, π+π−π± candidate, consistent with expected background in each channel. The following 90% confidence level upper limits are determined: View the MathML source and View the MathML source, where the ranges quoted correspond to the range of predicted Bc± lifetimes from 0.4 to 1.4 ps, and View the MathML source, constant over the range of predicted Bc± lifetimes.