Of course there are many subtle shades to play with in the spectrum of turquoise and chartreuse... from sky blue to teal, and from yellow-green to lime. You can tinker around with these to find the most complementary pair. If you want to go all out, choose the boldest shade of each; or, in order to temper the brightness, try pairing a paler shade of one color with a brighter or more saturated hue.
If you're ready to go big, consider a reupholstery project using a fabric in turquoise or chartreuse. These non-traditional colors are an especially fun contrast for a formal piece or an antique (see second photo).
If, on the other hand, you want to try the color combo without making a big investment, throw pillows and fresh flowers are a great way to get a sense for how you feel about bringing a bold color into your home. We love the green mums in the fourth photo against the bright blue velvet pillow.
Do you like this particular blue/green combo in your home? How do you make it work?