It is theoretically possible, but practically it would be difficult to get a clear hologram, and it's much easier to just split one beam into two.
The reason for this is that in order to produce a clear hologram we need the two laser beams to remain coherent with one another, so that they produce a clean, stable interference pattern. If the beams were almost coherent but not quite, you could still get some sort of hologram, but it would have aberrations and become fuzzier.
It's theoretically possible to make a totally separate beam maintain perfect coherence with the original beam, but it's far easier to simply use a beam splitter and obtain that coherence automatically.
As an analogy, think of it like the question: "Is it possible to project a negative image of yourself without a mirror?" Sure, it's possible---line up a bunch of LEDs or something in exactly the right pattern, or take a photo, reverse it on a computer, and project that on the screen. But it's much easier to just use a mirror.