The Sun's gradual brightening will seriously compromise the Earth'sbiosphere within ∼ 109 years. If Earth's orbit migrates outward,however, the biosphere could remain intact over the entiremain-sequence lifetime of the Sun. In this paper, we explore thefeasibility of engineering such a migration over a long timeperiod. The basic mechanism uses gravitational assists to (in effect)transfer orbital energy from Jupiter to the Earth, and therebyenlarges the orbital radius of Earth. This transfer is accomplishedby a suitable intermediate body, either a Kuiper Belt object or a mainbelt asteroid. The object first encounters Earth during an inward passon its initial highly elliptical orbit of large (∼ 300 AU)semimajor axis. The encounter transfers energy from the object to theEarth in standard gravity-assist fashion by passing close to theleading limb of the planet. The resulting outbound trajectory of theobject must cross the orbit of Jupiter; with proper timing, theoutbound object encounters Jupiter and picks up the energy it lost toEarth. With small corrections to the trajectory, or additionalplanetary encounters (e.g., with Saturn), the object can repeat thisprocess over many encounters. To maintain its present flux of solarenergy, the Earth must experience roughly one encounter every 6000years (for an object mass of 1022 g). We develop the details ofthis scheme and discuss its ramifications.