That time period between 1PM and 4PM when you rush frantically to your destination before rush hour comes. Failing to do so means being stuck in crawling traffic and doubling, possibly tripling you commute time. People who partake in the pre-rush hour rush are called "pre-rush hour rushers" for obvious reasons.
Example 1: When the police officer asked me why I drove twice the speed limit, he didn't take so kindly to me citing the pre-rush hour rush as an excuse.
Example 2: Yedid cuts all of her last classes short to avoid rush hour because she has to get home on time for her long AIM sessions with men old enough to be her father.