The Handel & Haydn Society uses period instruments and techniques in its orchestral, choral, and opera performances, yet it's as cutting-edge as any other ensemble in town. Established in 1815, it's the oldest continuously performing arts organization in the country. The company prides itself on its creative programming of "historically informed" concerts, which it stages from October through May, with most performances at Symphony Hall and New England Conservatory's Jordan Hall. Works by Handel and Haydn predominate but don't take up the entire schedule.
H&H gave the American premiere of Handel's Messiah, in 1818, and has made it an annual holiday tradition since 1854. If you'll be in town in December, check for ticket availability as soon as you start planning your trip.