Would it be theoretically possible for a planet to follow a perfectly circular orbit

Planets' orbital paths are ellipses that have low eccentricity. Would it be possible for a planet to have a circular orbit, since circles are simply ellipses with 0 eccentricity?

Only if:
1) Two bodies (one orbiting the other) were the only two objects in the universe.
2) The initial distance and orbital velocity were exactly correct. If the velocity varied by only 1 metre per second over the orbit, the path would be an ellipse, not a circle.
Points to note:
In 1) it would ber more accurate to say that the two bodies were orbiting their common centre of mass. A third body would perturb the orbits so as not to be circles and since gravity extends to infinity, that body could be anywhere.
In 2) this is not achievable in practice because if they remain within 1 metre per second velocity, are they within 10 cm/sec, 1 cm/sec, etc.?

Probably not.. All planets have some eccentricity to their orbits because as they orbit the star they are accelerated by the massive force exerted on them by the star, thereby created an elliptical orbit. Earth and some of the inner planets are said to have NEARLY circular orbits (notice the word nearly does not mean perfectly) but in fact the eccentricity of the orbits of all planets changes over long periods of time, even Earth's. The existence of a perfectly circular orbit is just simply too unlikely to exist, there are too many pushes and pulls out there to allow for a planet to stay in a perfect circle.

Yes that is theoretically possible. Even the earth has a nearly circular orbit around the sun during certain times of its revolutions around the sun. Circles are not ellipses but ellipses are elongated circles. Circles could be thought of as balanced ellipses. If any planet ever rotates around a star in a perfect circle it would only do so seasonally, that is during limited time periods of its existence.