the trick is making them flower at the same time. Since bur and chinkapin oaks are in the same family (white oaks) they should be able to produce a hybrid. I would just plant them next to each other and see what happens.

The way these nurseries get hybrids is by planting large number of acorns and finding seedlings that have characteristics that are different from the other seedlings. The acorns will appear like the rest but the seedlings growth habits/leaves will be very different from the non hybrids.

Joe,
Bur & chinkapin can and do hybridize, as they're both members of the white oak group. I had, at one point in time, a 'chinkabur' selection grafted & growing here, but have lost it along the way.

Essentially, you'd have to 'bag' the pistillate flowers prior to their becoming receptive in order to preclude pollenation by unknown sources and then pollenize them with mature catkins from the desired species, then re-bagging to prevent any 'interlopers'.
Not sure how many(if any) folks are actively breeding hybrid oaks, but the process would be similar for most fruit/nut breeding programs (USDA has a pecan-breeding program; granted, they're crossing cultivars of the same genus, but the process would be very similar for oaks of different species, within the same group).

I would love to see a Q. Virginiana X Q. Alba hybrid. That may never happen naturally because of native population not being close together. They may be close in a few tiny locations. I already have the Q. Lyrata X Q. Virginiana already. To OP I would ask a hybrid oak nursery, maybe Mossy oak natives nursery, how they know what they have when the trees are young. They have a lot of different hybrids.

Spent two days trying to find the book/article I recall. Gave up. Here's what I recall...

The only thing limiting oaks from freely hybridizing with any other species within the genus is overlapping a) habitat ranges and b) flowering times.

Considering the vast range of the quercus genus, some species will cross pollinate more freely than others. Want an exercise in beating your head against well, an oak tree? go for a walk in the woods and attempt to clearly discern to what species the different oak trees you find belong. Are the discrepancies due to variation within a species or to some degree of hybridization.

Oak hybridization programs tend to be rare, due in part to the long time frame from germination to seed production. Of the top of my head, while I know several nurseries that specialize in oaks/have extensive listings of a number of oak species...I can't say that I know of a breeding program in the traditional sense of following the generations. Most are just cross pollinating the closely related species and growing out the F1 generation. But then, when talking oaks...not exactly a popping demand for high quality acorns.

hey poaky how is your Compton oak doing?Does it retain its leaves in winter?

Greenthumbsdude, I have 3 Comptons oaks. The 2 that are not close to the house I haven't checked on for about 2 weeks because of snow/slush in the low area of the yard they are in but I have one about 40 ft approx to the house it has kept it's leaves (green also) last year a nd this year, which is as long as it's been here. If I* had to guess about the other 2 Comptons they probably lost their foliage. One of them had put out some tender new growth last fall which is probably ruined. But I am sure the tree will recover. Anyhoo, the trees are growing well. Last growing season they put out about 2 ft maybe more, I would definately recommend the Comptons to anyone who has room, they can get to be 80 ft plus spread possibly. Colonial Williamsburg has the biggest one. I am so far having good luck with a hybrid live oak Quercus Virginiana in my yard. It is a late seeding Q. Virginiana from Mossy oak natives nursery. I don't want to jinx myself by being too confident but SO FAR so good. Maybe I should make a circle of salt around myself to ward off bad luck. But seriously, I hope it makes it.

I once read that in most areas, nearly 100% of oaks are technically not "pure" even if identified as a particular species.

So if you find a tree identified as a Q. alba, there is a very, very good chance that at least some percentage (well under 25% if not clearly a hybrid) of its DNA could be Bur, Swamp White, Chinkapin, etc.

I think most hybrids are identified by analyzing leaf shape, buds, twigs, acorns, etc. but that is probably still never 100% without a DNA test.

I wonder if there is a DNA type test for trees. I know you can test your dog with a kit you swab saliva or some source of Genetic material and send in for the results. It's funny how some trees adapt to the area they're in and another tree that's supposed to be the same will croak. There is a late acorn dropping Q. Virginiana. I am trying it here in case it is a back-cross with the hardier Q. Fusiformis. I'm hoping for the size/ fast growth genetics of Q. Virginiana and hardiness of Q. Fusiformis. I know the OP was referrring to "controlled Hybridization" but Joeschmoe's post got me thinking about the Wild grown hybridization as well and I ran with it.

It would be awesome if someone created an all in one white oak. A hybrid of every species in the white oak family.

I've collected acorns off Quercus polymorpha (Mexican White Oak). I came up with interesting seedlings. One looked like White Oak with more evergreen??? They sure are fast growers. I would highly recommend it over Live oak if you want shade now plus it is more resistant to oak wilt.

All my Live oaks will be getting a test this week, it's supposed to go down to 6 F one night this coming week. I'm not worried about the Fusiformis much, but the new Virginiana X Fusiformis hybrids will be tested. My yard will be a couple degrees warmer, but at the downhill part it may really be 6 F.

hey poaky1 how are your live oaks?