It is an object to provide an inexpensive alloy for heat dissipation having a small thermal expansion coefficient as known composite materials, a large thermal conductivity as pure copper, and excellent machinability and a method for manufacturing the alloy. In particular, since various shapes are required of the alloy for heat dissipation, a manufacturing method by using a powder metallurgy method capable of supplying alloys for heat dissipation, the manufacturing costs of which are low and which take on various shapes, is provided besides the known melting method. The alloy according to the present invention is a Cu—Cr alloy, which is composed of 0.3 percent by mass or more, and 80 percent by mass or less of Cr and the remainder of Cu and incidental impurities and which has a structure in which particulate Cr phases having a major axis of 100 nm or less and an aspect ratio of less than 10 are precipitated at a density of 20 particles/μm2 in a Cu matrix except Cr phases of more than 100 nm.