The objective of this study was to determine the genetic parameters of methane (CH4) emissions and their genetic correlations with key production traits. The trial measured the CH4 emissions, at 5-min intervals, from 1225 sheep placed in respiration chambers for 2 days, with repeat measurements 2 weeks later for another 2 days. They were fed in the chambers, based on live weight, a pelleted lucerne ration at 2.0 times estimated maintenance requirements. Methane outputs were calculated for g CH4/day and g CH4/kg dry matter intake (DMI) for each of the 4 days. Single trait models were used to obtain estimates of heritability and repeatability. Heritability of g CH4/day was 0.29 ± 0.05, and for g CH4/kg DMI 0.13 ± 0.03. Repeatability between measurements 14 days apart were 0.55 ± 0.02 and 0.26 ± 0.02, for the two traits. The genetic and phenotypic correlations of CH4 outputs with various production traits (weaning weight, live weight at 8 months of age, dag score, muscle depth and fleece weight at 12 months of age) measured in the first year of life, were estimated using bivariate models. With the exception of fleece weight, correlations were weak and not significantly different from zero for the g CH4/kg DMI trait. For fleece weight the phenotypic and genetic correlation estimates were −0.08 ± 0.03 and −0.32 ± 0.11 suggesting a low economically favourable relationship. These results indicate that there is genetic variation between animals for CH4 emission traits even after adjustment for feed intake and that these traits are repeatable. Current work includes the establishment of selection lines from these animals to investigate the physiological, microbial and anatomical changes, coupled with investigations into shorter and alternative CH4 emission measurement and breeding value estimation techniques; including genomic selection.