This topic gets very complicated very quickly. Here's a short version. All life is made up of cells. All cells in the human body, except red blood cells, contain chromosomes.
Chromosomes got their name from the first lab experiments in the 1880s that revealed chromosomes could be easily stained with dyes, thus making studying them easier.
A gene is located on a chromosome. Every factor in inheritance is due to a particular gene. Genes specify the structure of particular proteins that make up each cell.
Gene comes from the Greek word genea meaning generation, origin, beginning, kin, or sometimes race. Gene was shortened from "pangene" which means "all-generation". Genes contain DNA (deoxyribonucleic acid). DNA is the chemical basis of heredity.
Think of it this way: DNA is in genes, genes are on chromosomes. When "mapping" all genes on all human chromosomes was first seriously conceived, it was called the Human Genome Project - a combination of gene and chromosome.