  Chern insulators, which are the lattice analogs of the quantum Hall states,
can potentially manifest high-temperature topological orders at zero magnetic
field to enable next-generation topological quantum devices. To date, integer
Chern insulators have been experimentally demonstrated in several systems at
zero magnetic field, but fractional Chern insulators have been reported only in
graphene-based systems under a finite magnetic field. The emergence of
semiconductor moir\'e materials, which support tunable topological flat bands,
opens a new opportunity to realize fractional Chern insulators. Here, we report
the observation of both integer and fractional Chern insulators at zero
magnetic field in small-angle twisted bilayer MoTe2 by combining the local
electronic compressibility and magneto-optical measurements. At hole filling
factor {\nu}=1 and 2/3, the system is incompressible and spontaneously breaks
time reversal symmetry. We determine the Chern number to be 1 and 2/3 for the
{\nu}=1 and {\nu}=2/3 gaps, respectively, from their dispersion in filling
factor with applied magnetic field using the Streda formula. We further
demonstrate electric-field-tuned topological phase transitions involving the
Chern insulators. Our findings pave the way for demonstration of quantized
fractional Hall conductance and anyonic excitation and braiding in
semiconductor moir\'e materials.
