Question: I have an idea that the seas of a world are red, not blue. However, the world should also be the birthplace of an intelligent alien species. Would it be scientifically possible to have a world with a red sea and where intelligent life can still develop?

Answer: 
There are two easy ways:

1. The color "blue" is partially a function of light reflected by the sky. If the sky is red to the human eye, say due to dust, the water will be reddish.
2. On Earth, Chlorophyll (the green component of plants) actually reflects more red light than green. Our eyes are more sensitive to the green light than the red, so it appears green to our eyes. Plants that have slightly different chlorophyll or higher proportions of other pigments, such as the algae that @jdunlop mentions, do appear red to the human eye.

**Edit**
In spite of my memory, chlorophyll does not reflect more red than green, even when fluorescence is allowed for. The only way this makes sense with plant pigments is with carotenes or other red pigments.
The reason our own ocean is blue is because of the color of the sky. If your sky is red/orange, you might end up with a red ocean. You could also do what a couple others have said and try an alga that's red.