Bad ground. Turn the headlights on, and check for voltage between the ground terminal of the headlight electrical connector and a good chassis ground or battery terminal. The headlight is probably grounding out through the turn signal.
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john

Which model do you have?

Did you check the 700/900 FAQ? Even if you do not have a 700/900, many of the same things in the FAQ apply to your car.

In a 740, I suggest that you check the grounds in your right front fender, A bad ground in the left front fender actually caused our 744 TI to stall when the high beams went on - crazy, but it is in the FAQ.

You might also check the left front fender as well. In my 745 TI, there are several grounds in the left front fender, including a ground in the frame for the antilock brakes assembly.

Anything that is mounted in plastic, such as a headlight, may have a ground wire - metallic items are grounded by their attachments to the engine or car body.

One easy way to check a ground is to add a temporary ground - directly to the ground side of the battery with a piece of wire.