We present a novel method of classifying Type Ia supernovae using convolutional neural networks, a neural network framework typically used for image recognition. Our model is trained on photometric information only, eliminating the need for accurate redshift data. Photometric data is pre-processed via 2D Gaussian process regression into two-dimensional images created from flux values at each location in wavelength-time space. These flux heatmaps of each supernova detection, along with uncertainty heatmaps of the Gaussian process uncertainty, constitute the dataset for our model. This preprocessing step not only smooths over irregular sampling rates between filters but also allows SCONE to be independent of the filter set on which it was trained. Our model has achieved impressive performance without redshift on the in-distribution SNIa classification problem: $99.73 pm 0.26$% test accuracy with no over/underfitting on a subset of supernovae from PLAsTiCCs unblinded test dataset. We have also achieved $98.18 pm 0.3$% test accuracy performing 6-way classification of supernovae by type. The out-of-distribution performance does not fully match the in-distribution results, suggesting that the detailed characteristics of the training sample in comparison to the test sample have a big impact on the performance. We discuss the implication and directions for future work. All of the data processing and model code developed for this paper can be found in the SCONE software package located at github.com/helenqu/scone.