Through our HARPS radial velocity survey for planets around solar twin stars, we have identified a promising Jupiter twin candidate around the star HIP11915. We characterize this Keplerian signal and investigate its potential origins in stellar activity. Our analysis indicates that HIP11915 hosts a Jupiter-mass planet with a 3800-day orbital period and low eccentricity. Although we cannot definitively rule out an activity cycle interpretation, we find that a planet interpretation is more likely based on a joint analysis of RV and activity index data. The challenges of long-period radial velocity signals addressed in this paper are critical for the ongoing discovery of Jupiter-like exoplanets. If planetary in nature, the signal investigated here represents a very close analog to the solar system in terms of both Sun-like host star and Jupiter-like planet.