Herpes Zoster (Shingles): Given the age of the patient and the location of the rash, Herpes Zoster is a highly likely diagnosis. It typically presents as a painful rash that follows a dermatomal distribution, which could easily involve the chest and back.

Contact Dermatitis: This could be due to an allergic reaction or irritant exposure, leading to a rash on the chest and back. The elderly may have increased susceptibility due to thinner skin and decreased barrier function.
Eczema (Atopic Dermatitis): Although more common in younger individuals, eczema can persist into old age or even start anew, presenting with itchy, inflamed skin that could appear on the chest and back.
Psoriasis: This chronic skin condition can cause red, scaly patches on various parts of the body, including the chest and back. While it often starts earlier in life, it can persist into old age.

Meningococcemia: Although rare, this condition can present with a rash and is life-threatening. It's crucial to consider, especially if the patient has fever, shock, or signs of meningitis.
Rocky Mountain Spotted Fever (RMSF): This tick-borne illness can cause a rash on the trunk, among other symptoms. Given its potential severity and the importance of early treatment, it should not be overlooked.
Stevens-Johnson Syndrome/Toxic Epidermal Necrolysis (SJS/TEN): These are severe skin conditions usually triggered by medications. They can present with widespread skin lesions and are medical emergencies.

Pemphigus: A group of autoimmune diseases that cause blistering of the skin and mucous membranes. While rare, they can be life-threatening and should be considered in the differential diagnosis of a rash, especially if there are oral lesions or significant blistering.
Cutaneous T-cell Lymphoma (Mycosis Fungoides): A rare form of skin cancer that can mimic various dermatological conditions, including eczema or psoriasis. It typically has a long, indolent course but can be aggressive in its later stages.