I am the shop manager of a non profit agency that provides job training for disables adults. We have a contract with a factory about 40 minutes away where we drive clients out to work for a day. We provide without cost to clients, transportation both ways. The clients do not begin work until they arrive at the factory. Do we have to pay them for the drive time?

Do you require the workers to ride the van? Or could they find another way to get to the client?
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.38.htm

So these employees are not your employees, but rather employees of the factory and your agency is just providing them transportation? If so, then no, you do not have to pay them for the time spent commuting.

Who the legal employer is might be worth verifying. I have worked for companies who have had a similar arrangement (on the customer side of things). The workers were the employees of the agency that trained them and the agency was the customer's vendor. I was on the AP side of things and we paid such vendors by the job. We never knew the names of the workers involved and indeed the specific workers tended to vary over time.

Also, the workers involved fall under a specific FLSA exception. As far as I know this is just (conditionally) a sub-minimum wage, although it is possible that the normal travel rules might also be affected. That might be something that federal DOL would have to be asked about, specifically if the very general 29 CFR 785.38 regulation applies to FLSA 14(c) workers.
http://www.dol.gov/esa/regs/compliance/whd/whdfs39.pdf

I am the shop manager of a non profit agency that provides job training for disables adults. We have a contract with a factory about 40 minutes away where we drive clients out to work for a day. We provide without cost to clients, transportation both ways. The clients do not begin work until they arrive at the factory. Do we have to pay them for the drive time?

No.

This is commute time, even if the agency is the employer.

But until the OP comes back and answers the question I posed, this time being compensable is still up in the air.