ORD Controller described a ground conflict when traffic; cleared via a runway; activated an ASDE-X alert approaching an active runway with a departure rolling; taxi speed was listed as a possible alert activation factor.

Narrative

Plan X; departing Runway 04L/09R/32R and Landing Runway 09; [and I was] working North Local Control. Aircraft X was taxied to Runway 32R Intersection V for departure. He was filed over EON which is a south bound fix. If I had departed him off of Runway 32R/V he would have stopped all my departures temporarily to get him turned southeast bound. I felt it would be easier to back taxi him to Runway 14L at U2 so I could depart him on a runway heading and he would not tie up any of my airspace. I instructed Aircraft X to taxi on Runway 32R and hold short of 04L as I had Air Carrier Y in position. Once my Runway 09R arrival had landed; I rolled Air Carrier Y off Runway 04L. During this time I was crossing Runway 09R with a heavy B767; loading Runway 09R with a departure; and ensuring the 09R lander was clearing the runway because I needed to get the 09R departure rolling soon because the next Runway 09R arrival was near the outer marker. Right as Air Carrier Y was going through the intersection of Runway 09R; I was getting ready to roll my next Runway 09R departure when my Local Assist instructed me to stop Aircraft X. Right when I began to key in to stop Aircraft X; the ASDE-X alerted and I instructed the traffic to stop. Air Carrier Y didn't seem to hesitate at all and continued with the take-off roll. Air Carrier Y departed without incident. Aircraft X appeared to be clear of the runway and Air Carrier Y never said anything when I shipped him over to departure. I then instructed Aircraft X to cross Runway 04L and had him exit the runway. Upon review of the ASDE-X data and a phone call from the pilots; Aircraft X was about 150 FT from the Runway 04L intersection. The speed of the taxi is what probably set off the ASDE-X and the pilots said they were going to get confirmation from me prior to crossing Runway 04L.