I saw online that they allow visitors (for a fee) to hold a young panda. Is this true?

YES， it is true. You can ask for that when you just arrive in the garden. For special reason, it is not allowed. Anyway, it is very expensive, 1000RMB to hold a yound panda and take picture with it.

Actually, there are two ways that you can get close to pandas. The 1st one is to adopt a panda. That is CNY50, 000 each year and CNY500,000 for whole life of the panda you have adopted. The 2nd one is to make a donation to giant panda. That is less expensive, only CNY1, 000. If you only want has a chance to hold a panda, you may choose this one. Or if you want to see the panda you adopted anytime during your adoption period, you may adopt one.
Usually, you can hold giant panda anytime if the panda’s condition is great. In one word, it is all depend on pandas. In general you can hold panda from 9:45am to 11am and 2:30pm to 4pm. If you still have problems concerning the tour in Chengdu or holding giant pandas, you may contact me by email any time. Then I will tell you the latest development.