I started my car up and watched the tach slowly climb up to 4 grand and then go back down to about 3800 and that is where it is stuck? Checked it at the distributor. It's an electric tach, what could be the problem?

 

I'm going to assume your vette is a '75 + here. Start with the simplest things. Check the fuses, check your ground. (at tach unit) Do a visual on all connectors involved.
-Continuity checks for tach signal starting @ the distributor (in order of circuit flow)
- Pop top off coil, coil to tach terminal
- Tach term to (most likely color's brown) tach wire
- Tach wire to tach unit
- Tach unit to black ground wire
- Grd wire to (clean metal contact) ground
-There's a hot power wire (pink or red) coming to the tach from the interior harness also. Check it's status and continuity. Now none of these include the illumination lamps. So if you pop a bulb out in your search, wrong circuit.
I believe that about 1977, printed circuits were used in place of wires at the back of the gages/instruments. These are rather fragile, and a common source of problems. If your vette includes this, I would look for broken runners (printed copper strips on mylar) here also. Also I believe that the tach filter is inside the tach unit itself, (depending on year) which is another component that could fail. If nothing shows fault in the connecting circuits, most likely then it's in the tach unit. Time to visit the repair shop, that specializes in instrument repair. A service manual and wiring diagram would be helpful to you with this. Hope this helps - Good Luck!