Theoretical estimates of the lifetime of the neutral π meson have indicated a value of the order of 10⁻¹⁷ secs. In order to determine the lifetime by flight distance measurements a method employing very fine resolution is required. Nuclear emulsions provide a medium for resolution of distances of the order of a micron. This experiment uses the same principle as that first tried by Harris et al.(1957). The decay at rest of the K⁺ meson in the K_π2 mode (π⁺π⁰) provides a π⁰ of unique velocity and a direction directly opposite to that of the π⁺; the latter being charged, leaves a track in the emulsion. The decay of the π⁰ is detected in emulsion if it takes place in the Dalitz mode:- π⁰ γ+e⁺+e⁻ (br. ratio 1.2%). Detection is possible because of the emission of charged particles. A stack of Ilford L4 emulsions was exposed to a beam of stopping K mesons. After processing, the stack was scanned for K_π2 decays with the emission of a Dalitz pair. Other π⁰ producing decays of the K⁺ (K_μ3, K_e3, τ′) were at first indistinguishable from the desired K_π2 decays. In order to reduce this contamination, grain density measurements were made on the charged secondary from the K⁺ decay. By rejecting events in which g* was greater than 1.3 all τ′ and 30% of the K_μ3 events were rejected. A correction factor was calculated to account for the remaining decays. The co-ordinates of the grains composing the events were measured relative to axes fixed in the field of view. A bifilar micrometer eyepiece was used which has the motions of the cross-wires digitised to enable rapid measurement. The co-ordinates were automatically punched out on to tape ready for input to the computer. The tracks of the particles were obtained by fitting straight lines to the measured co-ordinates. The decay point of the π⁰ was defined as the intersection of the electron tracks with the line of flight of the π⁺. The point of production was taken as the foot of the perpendicular from the measured position of the K⁺ on to the π⁺ trajectory. The effects of errors due to measurement, "grain noise" and grain size were thoroughly investigated. Use was made of co-ordinate measurements on τ decays of the K⁺ (π⁺π⁺π⁻) where it is known that the three tracks converge on the point of decay of the K⁺. An estimation of the lifetime was made using a likelihood calculation. It was discovered that the presence of events giving anomalous flight distances affected the estimate considerably. A suitable cutoff criterion was applied to reject these events.