A war between Greece and Bulgaria began because a dog crossed their border.

In 1925 during what would later be known as the Incident at Petrich, a Greek invasion of Bulgaria allegedly began with a Greek soldier chasing a runaway across the Bulgarian border. Bulgarian sentries shot the soldier, prompting a response from the Greek army. Greek forces invaded, and occupied the Bulgarian town of Petrich near the border.

Bulgaria appealed to the League of Nations to end the occupation. The Leage of Nations admonished Greece for the invasion, and ordered them to withdraw their troops and pay a fine. The conflict ended up taking the lives of over 50 people. This incident is also sometimes referred to as the "War of the Stray Dog".
(source)