Is muscle heavier than fat?

FAT VS MUSCLE

How does strength training help?

A pound of lean muscle will allow you to burn 50 additional calories a day.
A pound of fat burns nothing. If you build 5 pounds of muscle you will burn 250 extra calories a day. Multiply this by 365 days in a year and divide by 3,500 (the number of
calories in one pound). The result indicates that with this added muscle you will lose an extra 26 pounds in just one year.

(Ref: Jorge Cruise, a San Diego-based weight-loss specialist and author of 8
Minutes in the Morning)

The definitive answer is... muscle! This precise information tends to be mainly found in academic literature, but here is the exact answer and the references to verify and backed it up.

1. The density of mammalian skeletal muscle is 1.06 g/ml.
"... 1.06 g/cm-3 which is the density of mammalian skeletal muscle"
Source:

The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 56:B191-B197 (2001)
Specific Force Deficit in Skeletal Muscles of Old Rats Is Partially Explained by the Existence of Denervated Muscle Fibers
Melanie G. Urbancheka, Elisa B. Pickenb, Loree K. Kalliainenc & William M. Kuzon, Jr.a,d http://biomed.gerontologyjournals.org/cgi/content/full/56/5/B191#R23
Reference given by the authors: Mendez J, Keys A, 1960. Density& composition of mammalian muscle. Metabolism 9:184-188.)

2. The density of fat (adipose tissue) is about 0.9 g/ml
"...by multiplying the density of adipose tissue (0.9196 g/ml)"
Source:

Association of adiponectin and resistin with adipose tissue compartments, insulin resistance and dyslipidaemia
M. S. Farvid1, T. W. K. Ng2, D. C. Chan2, P. H. R. Barrett2 and G. F.
Watts2* http://www.blackwell-synergy.com/doi/abs/10.1111/j.1463-1326.2004.00410.x

In summary, research suggests that muscle density is 1.06 g/ml and fat density is (about) 0.9 g/ml. Thus, one litre of muscle would weigh 1.06 kg and one litre of fat would weigh 0.9 kg. In other words, muscle is about 18% denser than fat.