John E

I have little to add to the skeptics' responses -- I concur entirely.
1) The roller chain is reliable, efficient, lightweight, and versatile. I love my derailleur gears, and I have enjoyed riding a hybrid transmission, a 14-16-18-20 1/8" cogset on a standard AW Sturmey-Archer 3-speed hub.
2) The big current trend in automotive engines is away from timing belts and back to chains, precisely because almost every engine made today is of the "interference" type, in which the pistons at TDC will hit the valves if any are more than a tiny bit open.

The one-and-only argument in favor of a belt over a chain is corrosion, but salt air is probably hard on rubber, as well. Also, various cleaners and lubricants tend to degrade rubber, as does good old acid rain or photochemical smog.

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Except for my daughter-in-law's 2005 4-cylinder Toyota Camry, every car in our family has a timing belt, and we change them on a 7-year / 70K mi interval. [My elder son and I recently did a water pump and timing belt job on his 2002 Audi A4 1.8T; we'll do the same on my wife's 2001 VW Passat wagon while we still remember how to do the job in less than 5 hours. My 1996 Audi A4 2.8 is about due again, as well. On YouTube we found a great video of a guy doing an Audi timing belt job, including the radiator/headlight assembly "nose pull." He shot it at about 1 frame/min., which makes a very fast-moving 5-min. sequence when played back at normal video rates.]