There can be several causes for the swelling on the chest such as epidermal inclusion cyst, lipoma, abscess or fibroma. It would be difficult to diagnose without an examination.
An epidermal inclusion cyst is a sac like structure with skin debris inside. Lipomas are the most common soft tissue tumors and are slow-growing, benign in nature. They contain fat which forms lobulated soft masses enclosed by a thin fibrous capsule. Lipomas occur in 1% of the population. They presumably arise from fat that may occur in the back, hips, or neck in adults. These types of swellings are usually not malignant. Most of these are small subcutaneous in location and are removed for cosmetic reasons.
The treatment of cysts involves complete surgical excision with the capsule to prevent local recurrence. The therapy depends on the location and diagnosis of the swelling.
You should consult a dermatologist for a complete evaluation of the swelling as it is present since long time.