Helium (He) can be frozen, but not at normal atmospheric pressure.
More Info: At room temperature, liquid helium is the only element that cannot be frozen by lowering the temperature alone. It will ultimately solidify with the combination of a temperature and a pressure change. [“Chemistry of Helium ” UC Davis University of California]
To freeze helium, the pressure must be increased to approximately 25 atmospheres of pressure and the temperature reduced to near absolute zero. At this pressure, helium will begin to freeze if the temperature goes below 0.95 K (-272.2º C; -457.96º F). At normal atmospheric pressure, if the temperature of helium rises above 4.2 K (-268.9º C; -452.02º F) it will begin to boil (become a gas). Helium therefore can change states from gas, to liquid, and to a solid at temperatures near absolute zero and at high pressure. [“Helium” Chemicool.com]
Helium can also be forced to form a solid at room temperature if the pressure is increased to 114,000 atmospheres. This is equivalent to 1.67 million pounds per square inch or 834 tons per square inch. This pressure does not occur naturally on the Earth’s surface. [“Helium” Chemicool.com]
Freezing Helium 3
The above thermodynamic information applies to Helium 4 (He4), which represents greater than 99.999% of the helium found naturally on Earth. Helium 4 consists of two protons and two neutrons. Helium 3 (He3), which consists of two protons and only one neutron, represents 0.000137% of natural helium. He3 also behaves differently at low temperatures due to its lower mass. The boiling point of He3, which is 3.19 K, is about 1 K lower than He4. If pressure is increased to about 33 atmospheres, He3 will freeze at about 0.8-0.9 K. Since the nucleus of He3 spins, at this pressure the temperature must drop below 0.005 K before an ordered solid will form. [“Introduction to Liquid Helium.”NASA]
“Chemistry of Helium ” UC Davis University of California ChemWiki. N.p., n.d. Web. 2 Jan. 2013. http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Descriptive_Chemistry/Main_Group_Elements/Group_18%3A_The_Noble_Gases/Chemistry_of_Helium#Solid_and_liquid_phases.
“Helium.” Chemicool.com Periodic Table of Elements and Chemistry. N.p., n.d. Web. 2 Jan. 2013. http://www.chemicool.com/elements/helium.html.
“Introduction to Liquid Helium.”NASA Instrument Systems and Technology Division. N.p., n.d. Web. 2 Jan. 2013. http://istd.gsfc.nasa.gov/cryo/introduction/liquid_helium.html.