Help! Vibration when accelerating?

[1960chevypanel]

Have an '84 C20 454/turbo 400 rear wheel drive pickup with 65K og miles. She just started doing a deep/low vibration when I accelerate over 35mph. If I take my foot off the gas the vibration stops. The trans has never given me any problems, the fluid is pink and full. I just checked the u-joints visually and don't see any obvious problems, and don't feel any excessive play. Has anyone else had this issue? I'd like to brainstorm up a list of 5 or 6 things that I can check. Need to get the truck back on the road asap.