Would it be possible to put hydrogen into a vacuum chamber and use something to turn it into a smaller version of a star? I am making a scene with a simulated planet environment in space and wanted the core to be a very, very small star.
Yes, it is possible.
You can do it in an uncontrolled way in a hydrogen bomb,
Modern fusion weapons consist essentially of two main components: a nuclear fission primary stage (fueled by U-235 or Pu-239) and a separate nuclear fusion secondary stage containing thermonuclear fuel: the heavy hydrogen isotopes deuterium and tritium, or in modern weapons lithium deuteride. For this reason, thermonuclear weapons are often colloquially called hydrogen bombs or H-bombs
or in a controlled way in a reactor like ITER
The ITER thermonuclear fusion reactor has been designed to produce a fusion plasma equivalent to 500 megawatts (MW) of thermal output power for around twenty minutes while 50 megawatts of thermal power are injected into the tokamak, resulting in a ten-fold gain of plasma heating power.
Since you want it in the core of a planet, the ITER way seems the choice for you.
If your really want to simulate a star, you need enough gravity to hold the hydrogen (and "metals", the astromical term for anything that isn't hydrogen) together at sufficient density for fusion to take place.
Assuming you aren't going to drop a tiny black hole into the core of your synthetic star, you'd need a way to artificially generate gravity -- and then, probably, a way to shield against it, else the planet's own gravity, due to its mass, would be added to that used to contain the artificial star.
If all you're after is a heat source inside your planet, natural planet formation does this fairly well with the very large amounts (albeit tiny percentages) of natural radioactive elements incorporated into a planet's mantle and core. If you need your star to do something other than just heat the inside of the planet (say, act as the sun for a hollow world that breaks a bunch of physical laws), you'll have to do a lot of hand-waving.