The average density of oak is 680 kg/m3. I am making the assumption that the most a woodchuck can throw at once is gonna be the size of a large acorn. Anything above, the woodchuck probably cannot carry or throw. According to Wikipedia, the larger size acorns are about 24cm3.

A simple unit conversion will tell us that 24cm3 = .000024m3 . Given what we know already about the density of oak, 680kg*.000024m3 =.01632 kg. So, one large acorn sized piece of oak will weigh .01632 kg, or 16.32 grams.

There are 3.62455636m3 in 1 chord of wood. We also already found out that one piece of wood that the woodchuck can chuck is .01632m3 . 3.62455636m3 / .01632m3 =222.092914216 pieces of wood that a woodchuck would have to chuck to have chucked one chord of wood. We can just round up to 223 pieces of chucking wood in 1 chord of wood.

I will make another assumption that a woodchuck can chuck wood at a rate of one piece of wood per 5 seconds. To throw 223 pieces of wood would take the woodchuck 1115 seconds, or 18.6 minutes, but let's round up to 19. To conclude, the woodchuck would chuck at a rate of 1 chord per 19 minutes.