Instead of building a privacy fence, or a chain linked fence, why not create a living fence? First check your municipal ordinances for height limitations, however typically property-line planting is not restricted.
To define your backyard with a fence-line, or walls for your outdoor living space, start with fast growing evergreens like Arborvitae or Italian Cypress their columnar shape are perfect for a fence line. Or go with a layered variety of plants evergreen trees and shrubs along with perennials (like Rose of Sharon) to create a more natural effect. Add some hardscape for detail rock formations or waterscapes in with the plants. If you’re wanting to cover a fence quickly plant Ivy, Clematis or Hops there are a variety of vines to choose from for all three.