We have observed 150 double charge exchange events, π − + 7 Li → π + + anything , at an incident π − lab kinetic energy of 102 MeV. The π + were recorded in an emulsion stack at 30° to the incident π − beam. No significant peak due to the hypothetical reaction π − + 7 Li → π + + 7 H(g.s.) was observed in the part of the π + energy spectrum corresponding to a 7 H binding energy between −5 MeV and +25 MeV. Our new upper limit for the corresponding differential cross section is 1.0 × 10 −31 cm 2 sr (90% C.L.). The π + spectrum was recorded down to low energies (20 MeV < E π + < 100 MeV); its shape implies a strong final-state interaction among the π + , the proton and the six neutrons. The differential double charge exchange cross section integrated over all π + energies was determined as ( dσ dΩ ) tot = (4.2 ± 1.7) × 10 −30 cm 2 sr .