My answer to another question: "As we increase the size and mass of a world, at what point does it become impossible for a rocket to achieve an orbit or escape velocity?As we increase the size and mass of a world, at what point does it become impossible for a rocket to achieve an orbit or escape velocity?", answers this one quite well.
Depending upon what you're willing to pay for, it is well within the our technical capabilities to build a rocket that would accomplish this mission.
- The Earth's mass is the limit for a single stage chemical rocket to achieve orbit.
- A 3 stage chemical rocket, with performance similar to those we already have, could achieve orbit around a planet with Saturn's mass.
- A single stage nuclear pulse rocket could achieve orbit from a planet with mass around 6 times that of Jupiter.
- A 3 stage nuclear pulse rocket could achieve orbit from any planet and even low mass stars.
As others have pointed out, some of these solutions would be very costly indeed.