Conversation so far:
Did Tim Kaine run for Governor?
In 2005, Tim Kaine ran for governor of Virginia.
In which state did Tim Kaine run for Governor?
In 2005, Tim Kaine ran for governor of Virginia.
Did Tim Kaine win Governor of Virginia in 2005?
Kaine won the nomination, garnering 39.7% of the vote to Diamonstein's 31.4% and Jones' 28.9%.

Question: Who did he run against?
Self-contained rewrite: Who did Tim Kaine run against for Governor of Virginia in 2005?