  We investigate the specific heat of ultra-pure single crystals of Sr2RuO4, a
leading candidate of a spin-triplet superconductor. We for the first time
obtained specific-heat evidence of the first-order superconducting transition
below 0.8 K, namely divergent-like peaks and clear hysteresis in the specific
heat at the upper critical field. The first-order transition occurs for all
in-plane field directions. The specific-heat features for the first-order
transition are found to be highly sensitive to sample quality; in particular,
the hysteresis becomes totally absent in a sample with slightly lower quality.
These thermodynamic observations provide crucial bases to understand the
unconventional pair-breaking effect responsible for the first-order transition.
