Could be a ridiculous amount of play in your driveline. Specifically your diff.
Park your truck on level ground, block the wheels and put the parking brake on. Put the tranny in neutral and crawl under.
Grab the driveshaft and turn it back and forth. My Ranger has enough play that's it's almost a half turn from when it hits something CW to when it hits something CCW, my Explorer on the other hand has about 1/8 turn.
My Explorer rides mint, and my Ranger does exactly what your description seems like. When I take off from stopped the motor starts turning first, then the slack is taken up, then I start moving.
IF you have a normal amount of play on the rear driveshaft, put it in 4x4, and try grabbing the front driveshaft and turning it. If you have play in the front driveshaft, but little in the rear, then you could very well be right about a loose/damaged chain.