The attraction between two objects due to gravity is given by:

a = (m1+m2)/d^2

Mass changes with velocity, such that:

as v approaches c, m approaches infinity.

So, with a sufficiently distant object, a gravitational force acting on an object of mass m in a vacuum, the object will increase its velocity v towards the distant object. V will increase unbounded, as there is no counteracting force present. This means that m will increase unbounded as well, due to the relationship posited above.

Under normal reasoning, speeds greater than or equal to c are impossible, due to the impossibility of having an engine capable of moving infinite mass.

However, acceleration due to gravity increases with the mass of the object, so the motive force will be increasing proportionally to the mass. Indeed, the motive force will increase faster than the mass due to the effect of decreasing distance. So, as v increases towards c, and m increases towards infinity, a will also increase towards infinity, as m + m2 will approach infinity and d^2 will be approaching zero.

Is it then possible for gravity to accelerate an object past the speed of light?

You're using relativistic conditions with non-relativistic equations.

The equation you state is an approximation for speeds << c.

Have you studied relativity? If you use relativistic equations you will see that the speed of light is the limit.

It's past midnight here, so I don't have the brainpower to go into detail, but if you want me to I can do so another day?

I knew I had to be missing something important :)

I studied it briefly in Physics 3, which was split up roughly 1/2 optics, 1/3 thermo, and 1/6 relativity, but that's been five years and I really don't remember as much as I should (I remember most of the optics, though, and a good chunk of the thermo). Most of the relativity concepts that I remember are in the effects on time and spacial dimensions.

I'll have to dig out the old physics book and remind myself about all of it.

No need to go through it unless you just want to... I was just pondering that stuff instead of doing the work that I needed to be doing :)

Heh, ponderings are always fun to talk through :)