The three main things to consider when buying a second hand TVR Chimaera are: Condition, Condition and Condition. The other famous golden rule is "don't buy the first one you see". It's all too easy to get seduced by a shiny car and that awesome exhaust note.
What follows is a basic checklist of things to check when viewing a car. If you don't think you're up to this then you have other options. Take a look at James Agger or Rob Ingleby (in the Links section), they offer inspection services.
Take a look at the TVR Chimaera History page for more information on the car itself, the variations, engines and options. This should help to give you an idea of which model you'd be most interested in.
Also, it's well worth getting a copy of the Bible, it'll tell you loads more about the cars and it includes a more detailed buyer's guide.
Finally, you should seriously consider joining the TVR Car Club. The club offers many benefits which often cover the cost of membership. Importantly for someone considering a TVR, you can attend local meetings to get help and advice from other members. Also by looking at their cars (and getting a ride in one if you're lucky) you can get a better idea of what you're looking for.
The chassis have a habit of rusting on the outriggers behind the front wheels (especially on the nearside which tends to have a harder time). The factory coating seems to have quite a short life and even a newer car could have problems if poorly maintained. If possible get the car onto a ramp and have a poke around, ensure that the outriggers are solid. Signs of maintenance in the form of paint or waxoyl are a good sign.
Outrigger Corrosion (Blackpool Rot).
Check that the engine starts from cold and will idle without excessive hunting. Once warm ensure that the cooling system is working well. The car should run at around 80 degress while on the move and around 90 when stationary. Oil pressure should be around 25-30lbs. Once you've taken the car for a run leave the engine running and check that the cooling fans kick in at around 90 degrees. Once you're happy with the fans stop the engine and then restart to ensure that it's happy starting when hot, Finally give the oil cap a quick check for mayo.
Good news! No rust! Hurrah for fibre glass! This doesn't mean that you can ignore the bodywork. Stone chips are inevitable at the front and so re-sprays are common and nothing to worry about. Just be sure that any respray doesn't cover accident damage and is of a good quality. Panel fit should be quite good but the doors have been known to drop a little. Have a quick look at the windscreen, check for milkiness, delamination, chips or cracks.
Steering & Suspension
You can check the springs / dampers by pushing down on each corner. The car should return to it's position in one movement. Check the front ball joints by rocking the wheel while on the ground. Tyre wear can be a sign of suspension problems so ensure that the tyres we wearing evenly. Testing the steering by checking for any drift can tricky as the camber of the road can confuse the result. If the can pulls slightly to the left it's probably about right (or 'correct') if it pulls significantly to the right then there may be a problem.
Test everything so... windows, wipers, locks, alarm, heater fan, lights, indicators, stereo etc... If the dial backlights don't seem to be working check the button under the dash to the left of the steering wheel.
Clutch & Gearbox
Be sure that the clutch isn't slipping. Check that the gear change is smooth and precise. The later gearboxes are considered to be the best. Oh and if you get a crunch going into reverse then try going via 5th. (a case of "They all do that sir").
Wheels & Brakes
Ensure that the car brakes well and in a straight line. Check the wheels for scuffs. Tyres should be Bridgestone S02/S03s or at least Toyo ZRs, check the tread for excessive or uneven wear. There should be a spacesaver spare or at least some tyre-weld.
Servicing should have been conducted at least every year / 6000 miles. Look for stamps from TVR dealers or recognised specialists.